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  • 1.
    Aspenberg, David
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Jergeus, Johan
    Volvo Cars Safety Centre, Göteborg.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Robust optimisation of front members in a full frontal car impactManuscript (preprint) (Other academic)
    Abstract [en]

    In the search of a lightweight design of automobiles, it is necessary to assure that a robust crashworthiness performance is achieved. Structures that are optimised to handle a finite number of load cases may perform poorly when subjected to various dispersions. Thus, uncertainties must be accounted for in the optimisation process. This paper presents an approach to optimisation where all design evaluations include an evaluation of the robustness. Metamodel approximations are applied both to the design space and the robustness evaluations, using Artifical Neural Networks and polynomials, respectively. The features of the robust optimisation approach are displayed in an analytical example, and further demonstrated in a large scale design example of front side members of a car. Different optimisation formulations are applied and it is shown that the proposed approach works well. It is also concluded that a robust optimisation puts higher demands on the FE model performance than normally.

  • 2.
    Aspenberg, David
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology. Linkoping Univ, Div Solid Mech, SE-58183 Linkoping, Sweden .
    Jergeus, Johan
    Volvo Cars Safety Centre, Sweden .
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Robust optimization of front members in a full frontal car impact2013In: Engineering optimization (Print), ISSN 0305-215X, E-ISSN 1029-0273, Vol. 45, no 3, p. 245-264Article in journal (Refereed)
    Abstract [en]

    In the search for lightweight automobile designs, it is necessary to assure that robust crashworthiness performance is achieved. Structures that are optimized to handle a finite number of load cases may perform poorly when subjected to various dispersions. Thus, uncertainties must be accounted for in the optimization process. This article presents an approach to optimization where all design evaluations include an evaluation of the robustness. Metamodel approximations are applied both to the design space and the robustness evaluations, using artifical neural networks and polynomials, respectively. The features of the robust optimization approach are displayed in an analytical example, and further demonstrated in a large-scale design example of front side members of a car. Different optimization formulations are applied and it is shown that the proposed approach works well. It is also concluded that a robust optimization puts higher demands on the finite element model performance than normally.

  • 3.
    Aspenberg, David
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Larsson, Rikard
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    An evaluation of the statistics of steel material model parameters2012In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 212, no 6, p. 1288-1297Article in journal (Refereed)
    Abstract [en]

    In robustness studies, variations of material properties are often represented by simple assumptions, such as scaling of stress-strain relations, often due to lack of knowledge or deeper understanding of the material physics and the material model applied. By performing material characterisation tests on several batches of a DP600 steel and fitting a phenomenological material model to each batch, this paper studies the dispersion of material model parameters, as well as correlations between both experimental and model parameters. It is concluded that some of the charcterisation tests may be omitted in the future, due to correlations found between parameters. The results may also be applied in a robustness study by inversely using the retrieved statistics to generate reasonable new sets of material model parameters. The methodology presented may be adopted for any other type of material characterisation process.

  • 4.
    Björklund, Oscar
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Govik, Alexander
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Prediction of fracture in a dual-phase steel subjected to non-linear straining2014In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 214, no 11, p. 2748-2758Article in journal (Refereed)
    Abstract [en]

    In this work, selected fracture criteria are applied to predict the fracture of dualphase steel subjected to non-linear strain paths. Furthermore, the effects of manufacturing history are studied. Four fracture criteria were calibrated in three tests using standard specimens. The fracture criteria were first validated in the circular Nakajima test. A second validation test case was included in order to validate fracture prediction for non-linear strain paths. In this test a sheet metal component was manufactured and subsequently stretched until it fractured. All fracture criteria included in this study predict fracture during the Nakajima test with reasonable accuracy. In the second validation test however, the different fracture criteria show considerable diversity in accumulated damage during manufacturing which caused substantial scatter of the fracture prediction in the subsequent stretching. This shows that manufacturing history influences the prediction of fracture.

  • 5.
    Björklund, Oscar
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Larsson, Rikard
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Failure of high strength steel sheets: Experiments and modelling2013In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 213, no 7, p. 1103-1117Article in journal (Refereed)
    Abstract [en]

    Failure in sheet metal structures of ductile material is usually caused by one of, or a combination of, ductile fracture, shear fracture or localised instability. In this paper the failure of the high strength steel Docol 600DP and the ultra high strength steel Docol 1200M is explored. The constitutive model used in this study includes plastic anisotropy and mixed isotropic-kinematic hardening. For modelling of the ductile and shear fracture the models presented by Cockroft–Latham and Bressan–Williams have been used. The instability phenomenon is described by the constitutive law and the finite element (FE) models. For calibration of the failure models and validation of the results, an extensive experimental series has been conducted including shear tests, plane strain tests and Nakajima tests. The geometries of the Nakajima tests have been chosen so that the first quadrant of the forming limit diagram (FLD) were covered. The results are presented both in an FLD and using prediction of force–displacement response of the Nakajima test employing element erosion during the FE simulations. The classical approach for failure prediction is to compare the principal plastic strains obtained from FE simulations with experimental determined forming limit curves (FLCs). It is well known that the experimental FLC requires proportional strains to be useful. In this work failure criteria, both of the instability and fracture, are proposed which can be used also for non-proportional strain paths.

  • 6.
    Björklund, Oscar
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Anisotropic fracture criteria for a dual-phase steel2014Manuscript (preprint) (Other academic)
    Abstract [en]

    The main objective of this work is to examine the use of anisotropic fracture criteria in order to predict fracture in dual-phase steel. The introduction of a material directional function into the fracture criterion was used in order to account for anisotropy observed in experiments. Selected fracture criteria were fist calibrated by ordinary tensile and in-plane shear tests using specimens cut in three material directions. In order to validate the performance, two types of validation tests were conducted. First, plane strain (notched tensile) tests were carried out in three material directions. Second, Nakajima tests with a waist of 130 mm were conducted, also in three material directions. The fit to the calibration tests was improved with all material directional functions compared to the isotropic criterion. Overall best performance was achieved when a material direction function based on the structural tensors was introduced.

  • 7.
    Björklund, Oscar
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Failure characteristics of a dual-phase steel sheet2014In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 214, p. 1190-1204Article in journal (Refereed)
    Abstract [en]

    Failure in ductile sheet metal structures is usually caused by one, or a combination of, ductile tensile fractures, ductile shear fractures or localised instability. In this paper the failure characteristics of the high strength steel Docol 600DP are explored. The study includes both experimental and numerical sections. In the experimental sections, the fracture surface of the sheet subjected to Nakajima tests is studied under the microscope with the aim of finding which failure mechanism causes the fracture. In the numerical sections, finite element (FE) simulations have been conducted using solid elements. From these simulations, local stresses and strains have been extracted and analysed with the aim of identifying the fracture dependency of the stress triaxiality and Lode parameter.

  • 8.
    Borg, Rikard
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Borg, Rikard
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Simonsson, Kjell
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Simonsson, Kjell
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Simulation of delamination in fiber composites with a discrete cohesive failure model2001In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 61, no 5, p. 667-677Other (Other (popular science, discussion, etc.))
    Abstract [en]

    Delamination initiation and growth are analyzed by using a discrete cohesive crack model. The model is derived by postulating the existence of a maximum load surface which limits the adhesive forces in the process zone of the crack. The size of the maximum load surface is made dependent on the amount of dissipated crack opening work such that the maximum load surface shrinks to zero as a predefined amount of work is consumed. Mode I, II, III loading or any combined loading is possible. The delamination model is implemented in the explicit finite-element code LS-DYNA and simulation results are found to be in agreement with experimental results. ⌐ 2001 Elsevier Science Ltd. All rights reserved.

  • 9.
    Borg, Rikard
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
    Simonsson, Kjell
    Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
    Modeling of delamination using a discretized cohesive zone and damage formulation2002In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 62, no 10-11, p. 1299-1314Article in journal (Refereed)
    Abstract [en]

    Delamination initiation and growth are analyzed by using a discrete cohesive crack model. The delamination is constrained to grow along a tied interface. The model is derived by postulating the existence of a maximum load surface which limits the adhesive forces in the process zone of the crack. The size of this maximum load surface is made dependent on the amount of dissipated crack opening work, such that the maximum load surface shrinks to zero as a predefined amount of work is consumed. A damage formulation is used to reduce the adhesive forces. Mode I, II and III loading or any combined loading is possible. An analytical solution is obtained for a single mode opening and the implications of this result on the governing equations is discussed. The delamination model is implemented in the finite element code LS-DYNA and simulation results are shown to be in agreement with experimental results. © 2002 Elsevier Science Ltd. All rights reserved.

  • 10.
    Borg, Rikard
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Simonsson, Kjell
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Simulating DCB, ENF and MMB experiments using shell elements and a cohesive zone model2004In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 64, no 2, p. 269-278Article in journal (Refereed)
    Abstract [en]

    A delamination model for shell elements is presented. It consists of an adhesive penalty contact formulation for initially tying shells together and a cohesive zone model for degrading the adhesive forces. An adhesive contact used between shell elements has to account for the thickness offset, such that the rotational degrees of freedom in the shell elements are included in the algorithm. This is considered in the present contact model and the complete delamination model is implemented in the explicit Finite Element code LS-DYNA. By preventing delamination growth the delamination model can be turned into a tied contact. As such it is used in two FE-models, where plates are bonded together and subjected to various loads. The adhesive penalty contact performs well. The complete delamination is validated by simulating the Double Cantilever Beam, End-Notch Flexural and Mixed Mode Bending setups, and the results are shown to be in agreement with experimental data.

  • 11.
    Borg, Rikard
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Simonsson, Kjell
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Simulation of low velocity impact on fiber laminates using a cohesive zone based delamination model2004In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 64, no 2, p. 279-288Article in journal (Refereed)
    Abstract [en]

    An existing delamination model is further developed for use in transverse impact simulations. An algorithm is developed making it possible to determine the propagation direction of the delamination front. Using this it is possible to determine relative orientation of the delamination front with respect to the fibers above and below the interface. In a qualitative evaluation it is shown that the present delamination model can be used for modeling delamination initiation and growth in transverse impact simulations.

  • 12. Brandt, Jan
    et al.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    A consutitutive model for compaction of granular media, with account for deformation induced anisotropy2000In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 4, p. 391-418Article in journal (Refereed)
  • 13.
    Domeij Bäckryd, Rebecka
    et al.
    Linköping University, Faculty of Science & Engineering. Linköping University, Department of Management and Engineering, Solid Mechanics.
    Ryberg, Ann-Britt
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering. Combitech AB, Trollhättan, Sweden.
    Nilsson, Larsgunnar
    Linköping University, Faculty of Science & Engineering. Linköping University, Department of Management and Engineering, Solid Mechanics.
    Multidisciplinary design optimisation methods for automotive structures2017In: International Journal of Automotive and Mechanical Engineering, ISSN 2229-8649, Vol. 14, no 1, p. 4050-4067Article in journal (Refereed)
    Abstract [en]

    Multidisciplinary design optimisation (MDO) can be used as an effective tool to improve the design of automotive structures. Large-scale MDO problems typically involve several groups who must work concurrently and autonomously in order to make the solution process efficient. In this article, the formulations of existing MDO methods are compared and their suitability is assessed in relation to the characteristics of automotive structural applications. Both multi-level and single-level optimisation methods are considered. Multi-level optimisation methods distribute the design process but are complex. When optimising automotive structures, metamodels are often required to relieve the computational burden of detailed simulation models. The metamodels can be created by individual groups prior to the optimisation process, and thus offer a way of distributing work. Therefore, it is concluded that a single-level method in combination with meta-models is the most straightforward way of implementing MDO into the development of automotive structures. If the benefits of multi-level optimisation methods, in a special case, are considered to compensate for their drawbacks, analytical target cascading has a number of advantages over collaborative optimisation, but both methods are possible choices.

  • 14.
    Fjällström, Per-Olof
    et al.
    Linköping University, Department of Computer and Information Science, ACTLAB - Laboratory for Complexity of Algorithms. Linköping University, The Institute of Technology.
    Petersson, Jan
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Mechanical Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Zhong, Zhi-Hua
    Evaluation of Range Searching Methods for Contact Searching in Mechanical Engineering1998In: International Journal of Computational Geometry & Applications, ISSN 0218-1959, Vol. 8, no 1, p. 67-83Article in journal (Refereed)
    Abstract [en]

    Contact searching is an important and time-consuming part of computer simulation of certain deformation processes. Contact searching can be facilitated by orthogonal range searching. We have experimentally evaluated four methods for orthogonal range searching: the projection method, the cell method, the k-d tree method, and the range tree method.

     

    The results of our experiments indicate that two of these methods, the cell and k-d tree methods, have practical significance. The cell method is in most cases faster than the k-d tree method.

  • 15.
    Forsberg, Jimmy
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Evaluation of response surface methodologies used in crashworthiness optimization2006In: International Journal of Impact Engineering, ISSN 0734-743X, E-ISSN 1879-3509, Vol. 32, no 5, p. 759-777Article in journal (Refereed)
    Abstract [en]

    Optimization of car structures is of great interest to the automotive industry. This work is concerned with structural optimization of a car body with the intent to increase the crashworthiness properties of the vehicle or decrease weight with the crashworthiness properties unaffected. In this work two different methodologies of constructing an intermediate approximation to the optimization problem are investigated, i.e. classical response surface methodology and Kriging. The major difference between the two methodologies is how the residuals between the true function value and the polynomial surface approximation value at a design point are treated.

    Several different optimization problems have been investigated, both analytical problems as well as finite element impact problems.

    The major conclusion is that even if the same kind of updating scheme is used both for Kriging and linear classic response surface methodology, Kriging improves the sequential behaviour of the optimization algorithm in the beginning of the optimization process. Problems may occur if a constraint is violated after several iterations and then classic response surface methodology seems to more easily be able to find a design point which satisfies the constraint.

  • 16.
    Forsberg, Jimmy
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    On polynomial response surfaces and Kriging for use in structural optimization of crashworthiness2005In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 29, no 3, p. 232-243Article in journal (Refereed)
    Abstract [en]

    The accuracy of different approximating response surfaces is investigated. In the classical response surface methodology (CRSM) the true response function is usually replaced with a low-order polynomial. In Kriging the true response function is replaced with a low-order polynomial and an error correcting function. In this paper the error part of the approximating response surface is obtained from “simple point Kriging” theory. The combined polynomial and error correcting function will be addressed as a Kriging surface approximation.

    To be able to use Kriging the spatial correlation or covariance must be known. In this paper the error is assumed to have a normal distribution and the covariance to depend only on one parameter. The maximum-likelihood method is used to find the latter parameter. A weighted least-square procedure is used to determine the trend before simple point Kriging is used for the error function. In CRSM the surface approximation is determined through an ordinary least-square fit. In both cases the D-optimality criterion has been used to distribute the design points.

    From this investigation we have found that a low-ordered polynomial assumption should be made with the Kriging approach. We have also concluded that Kriging better than CRSM resolves abrupt changes in the response, e.g. due to buckling, contact or plastic deformation.

  • 17.
    Forsberg, Jimmy
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    The optimisation process of an energy absorbing frontal underrun protection device2008In: International Journal of Vehicle Design, ISSN 0143-3369, E-ISSN 1741-5314, Vol. 46, no 3, p. 271-293Article in journal (Refereed)
    Abstract [en]

    This paper describes the methodology used during the development of an energy absorbing Frontal Underrun Protection device (eaFUP). The aim of this study is to show how different optimisation methods can be used at different stages during the design process. It also shows one approach to derive an optimal design taking several different design alternatives into account, each of which consists of several different materials. The outcome of the optimisation process is three different designs of the eaFUP.

  • 18.
    Govik, Alexander
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Moshfegh, Ramin
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    The effects of forming history on sheet metal assembly2014In: International Journal of Material Forming, ISSN 1960-6206, E-ISSN 1960-6214, Vol. 7, no 3, p. 305-316Article in journal (Refereed)
    Abstract [en]

    As demand for faster product development increases, physical prototypes are replaced by virtual prototypes. By using finite element simulations to evaluate the functional behaviour of the product as well as its manufacturing process, more design alternatives can be evaluated while a considerably smaller number of physical prototypes are needed. As sheet metal assemblies are common in a wide range of products, reliable methods for predicting their properties are necessary. By sequentially simulating the complete manufacturing process chain of an assembly, early predictions concerning the geometry and material properties of the assembly can be made.

    In this study a simulation-based sensitivity study is performed in order to investigate the influence of the forming history on the predictions of assembly properties. In the study, several simulations of the assembly stage are performed in which different types of forming histories are retained from the forming stage. The simulations of the assembly stage will range from a case with linear elastic conditions without forming history, to a case with the full forming history state and consistent material modelling throughout all simulations. It is found that the residual stress state is the most influential history variable from the forming stage. Especially for more complex geometries in which large residual stresses can be retained.

  • 19.
    Govik, Alexander
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Andersson, Alf
    Chalmers University of Technology, Department of Product and Production Development, Gothenburg, Sweden.
    Moshfegh, Ramin
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Simulation of the forming and assembling process of a sheet metal assembly.2011Conference paper (Refereed)
  • 20.
    Govik, Alexander
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Moshfegh, Ramin
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology. Outokumpu Stainless AB, Avesta, Sweden.
    Finite element simulation of the manufacturing process chain of a sheet metal assembly2012In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 212, no 7, p. 1453-1462Article in journal (Refereed)
    Abstract [en]

    An increasing number of components in automotive structures are today made from advanced high strength steel (AHSS). Since AHSS demonstrates more severe springback behaviour than ordinary mild steels, it requires more efforts to meet the design specification of the stamped parts. Consequently, the physical fine tuning of the die design and the stamping process can be time consuming. The trial-and-error development process may be shortened by replacing most of the physical try-outs with finite element (FE) simulations of the forming process, including the springback behaviour. Still it can be hard to identify when a stamped part will lead to an acceptable assembly with respect to the geometry and the residual stress state. In part since the assembling process itself will distort the components. To resolve this matter it is here proposed to extend the FE-simulation of the stamping process, to also include the first level sub-assembly stage. In this study a methodology of sequentially simulating each step in the manufacturing process of an assembly is proposed. Each step of the proposed methodology is described, and a validation of the prediction capabilities is performed by comparing with a physically manufactured assembly. The assembly is composed of three sheet metal components made from DP600 steel which are joined by spot welding. The components are designed to exhibit severe springback behaviour in order to put both the forming and subsequent assembling simulations to the test. The work presented here demonstrates that by using virtual prototyping it is possible to predict the final shape of an assembled structure.

  • 21.
    Govik, Alexander
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Moshfegh, Ramin
    Linköping University, Department of Management and Engineering, Energy Systems. Linköping University, The Institute of Technology.
    Stochastic analysis of a sheet metal assembly considering its manufacturing process2014Manuscript (preprint) (Other academic)
    Abstract [en]

    In order to accurately predict the mechanical properties of a sheet metal assembly it has been shown important to account for how the geometry and material properties are affected by the manufacturing process. It is also of a great interest to predict the variations of important responses, and how these variations depend on the manufacturing process.

    In this study, the variation of properties during the multi-stage manufacturing process of a sheet metal assembly is evaluated and the variability of a response due to loading is studied. A methodology to investigate how variations evolve during the assembling process is presented. The multi-stage assembling process is virtually segmented, such that stochastic analyses of each process stage are performed and coupled to succeeding stages in order to predict the variation in properties of the final assembly. The methodology is applied to an industrial assembly and experimental validations have been conducted. The prediction of the geometry of the final assembly is in good agreement with the experimental results, while the prediction of the variation of this geometry is in fair agreement.

  • 22.
    Govik, Alexander
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Rentmeester, Rikard
    Saab AB, Linköping, Sweden.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    A study of the unloading behaviour of dual phase steel2014In: Materials Science & Engineering: A, ISSN 0921-5093, E-ISSN 1873-4936, Vol. 602, p. 119-126Article in journal (Refereed)
    Abstract [en]

    It is important to understand the strain recovery of a steel sheet in order to predict its springback behaviour. During strain recovery, the stress–strain relation is non-linear and the resulting unloading modulus is decreased. Moreover, the unloading modulus will degrade with increasing plastic pre-straining. This study aims at adding new knowledge on these phenomena and the mechanisms causing them. The unloading behaviour of the dual-phase steel DP600 is characterised experimentally and finite element (FE) simulations of a representative volume element (RVE) of the microstructure are performed. The initial stress and strain state of the micromechanical FE model is found by a simplified simulation of the annealing processes. It is observed from the experimental characterisation that the decrease of the initial stiffness of the unloading is the main reason for the degrading unloading modulus. Furthermore, the developed micromechanical FE model exhibits non-linear strain recovery due to local plasticity caused by interaction between the two phases.

  • 23.
    Jansson, Mikael
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    On constitutive modeling of aluminum alloys for tube hydroforming applications2005In: International Journal of Plasticity, ISSN 0749-6419, Vol. 21, no 5, p. 1041-1058Article in journal (Refereed)
    Abstract [en]

    The increased interest in lightweight materials for automotive structures has also lead to a search for efficient forming methods that suit these materials. One attractive concept is to use hydroforming of aluminum tubes. The advantages of this forming method includes better tolerances, decreased number of parts and an increased range of forming options. By using FE simulations, the process can be optimized to reduce the risk for failure, i.e. bursting or wrinkling. However, extruded aluminum is highly anisotropic and it is crucial that the material model used for simulations is able to accurately describe this behavior. Also, tube hydroforming occurs predominantly in a biaxial stress state which should be considered in the material testing, where uniaxial tests are used extensively in the industry today. The present study accentuates the need for improved constitutive models. It is shown that a material model, which accurately describes the anisotropic behavior of aluminum tubes, can be obtained from simple and robust experiments.

  • 24.
    Jansson, Mikael
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    On process parameter estimation for the tube hydroforming process2007In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 190, no 1-3, p. 1-11Article in journal (Refereed)
    Abstract [en]

    Tube hydroforming is a forming process where an inner pressure combined with axial feeding deforms the tube to the shape of a die cavity. One of the main concerns when designing such a process is to avoid burst pressure, i.e. the process state where the hardening of the material is unable to resist the increase in inner pressure and wall thickness reduction. The success of a hydroforming process strongly depends on the choice of process parameters, i.e. the combination of material feeding and inner pressure. Especially in hydroforming processes, where the free forming phase is substantial, the process is proved to be very sensitive to the inner pressure. By transforming the problem into a deformation controlled rather than a force controlled process, the results from the process parameter estimation become more reliable but on the other hand less intuitive. In this context, three distinct parameter estimation procedures are suggested. Firstly, a self feeding based procedure is proposed with the intention of being a fast method to be used as a first estimate of suitable process parameters. Secondly, an iterative optimization problem set up is presented. Thirdly, and finally, an adaptive simulation procedure based on process response approximations is proposed, which only requires a limited number of simulation runs.

  • 25.
    Jansson, Mikael
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    On strain localisation in tube hydroforming of aluminium extrusions2008In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 195, no 1-3, p. 3-14Article in journal (Refereed)
    Abstract [en]

    One important issue when simulating tube hydroforming is to predict bursting, i.e. when the increase in cavity pressure cannot be compensated by hardening of the tube material. Traditionally, this is made by a forming limit diagram (FLD), where the limit strains determine whether a material point is experiencing necking or failure. However, the experimental FLD depends on the strain path, and the methods which are used to determine the FLD are adapted to conventional deep drawing which, depending on the process characteristics, could make it unsuitable for tube hydroforming applications. In this work, analytical and numerical forming limit predictions are studied from a hydroforming point of view. These predictions are then applied to free bulge cases, and a case with extensive feeding in a die where the results from the latter case is compared to experiments. Further, the influence from extrusion welds and a circumferential thickness distribution on the forming limit is also evaluated.

  • 26.
    Jansson, Mikael
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    The use of biaxial test data in the validation of constitutive descriptions for tube hydroforming applications2007In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 184, no 1-3, p. 69-76Article in journal (Refereed)
    Abstract [en]

    When considering finite element simulations of aluminium tube hydroforming, the user is facing several challenges. Firstly, extruded aluminium is anisotropic in yield stress and plastic flow. Secondly, the hydroforming process introduces new issues concerning friction and process control. This imposes a demand for accurate constitutive models as well as for hydroforming process related testing methods. The present study focuses on how biaxial tests can be used to calibrate and validate a constitutive model. It is also shown that by using inverse modelling, additional information can be obtained through these types of tests, such as, e.g. the frictional behaviour for different lubrication conditions.

  • 27.
    Jansson, Mikael
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Tube hydroforming of aluminium extrusions using a conical die and extensive feeding2008In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 198, no 1-3, p. 14-21Article in journal (Refereed)
    Abstract [en]

    Tube hydroforming is gaining increasing interest from the metal forming industry. Complicated parts with a high level of structural component integration, e.g. engine cradles, subframes and exhaust systems, can be manufactured at a low cost with excellent repeatability. By using finite element (FE) simulations, there is a possibility to reduce the cost of expensive prototypes and reduce the trial and error design process to a minimum. However, when simulating a hydroforming process, the knowledge and computational methods used in conventional metal forming simulations are not always applicable. This concerns, e.g. the material modelling and validation. In this work, the influence of constitutive modelling on the results from a hydroforming process with extensive feeding is studied. In addition, interrupted tests have been used in order to validate the prediction of radial deformation and wall thickness throughout the complete process.

  • 28.
    Jansson, Tomas
    et al.
    Linköping University, Department of Mechanical Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Andersson, A.
    Volvo Car Corporation, Body Components, Olofström, Sweden and the Division of Production and Materials Engineering, Lund University, Sweden.
    Nilsson, Larsgunnar
    Linköping University, Department of Mechanical Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Optimization of draw-in for an automotive sheet metal part: an evaluation using surrogate models and response surfaces2005In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 159, no 3, p. 426-434Article in journal (Refereed)
    Abstract [en]

    In the present paper, an optimization of the draw-in of an automotive sheet metal part has been carried out using response surface methodology (RSM) and space mapping technique. The optimization adjusts the draw bead restraining force in the model such that the draw-in in the FE-model corresponds to the draw-in in the physical process. The conclusion of this study is that space mapping is a very effective and accurate method to use when calibrating the draw-in of a sheet metal process. In order to establish draw bead geometry from the draw bead restraining force a 2D-model was utilized. The draw bead geometry found showed good agreement with the physical draw bead geometry.

  • 29.
    Jansson, Tomas
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Minimizing the risk of failure in a sheet metal forming process: optimization using space mapping with one-step and incremental solvers2006In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 31, no 4, p. 320-332Article in journal (Refereed)
    Abstract [en]

    In the present paper, an optimization technique has been used to minimize the risk of failure in a sheet metal forming process. Two different types of finite element solvers, one using total plasticity and the other using incremental plasticity, have been used. A comparison between response surface methodology and space mapping (SM) with the one-step solver as surrogate model has been done. The conclusion of this study is that the use of the total plasticity theory drastically reduces the required computing time. Furthermore, the solution from the SM optimization algorithm is close to the solution obtained by the incremental plasticity solver.

  • 30.
    Jansson, Tomas
    et al.
    Linköping University, Department of Mechanical Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Optimizing sheet metal forming processes: using a design hierarchy and response surface methodology2006In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 178, no 1-3, p. 218-233Article in journal (Refereed)
    Abstract [en]

    In the present paper optimization has been used to evaluate alternative sheet metal forming processes. Six process set-ups were first defined in a hierarchy of designs and optimization was then used to evaluate each forming process of these designs. The challenge in designing the forming process was to avoid failure in the material and at the same time reach an acceptable through thickness strain. The conclusions of this study is that there may exist a different process that can give an improved product for the desired geometry. This process might be impossible for the optimization algorithm to reach due to either a poor starting point or a not so wise process set-up.

  • 31.
    Jansson, Tomas
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Redhe, Marcus
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Using surrogate models and response surfaces in structural optimization: with application to crashworthiness design and sheet metal forming2003In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 25, no 2, p. 129-140Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to determine if the Space Mapping technique using surrogate models together with response surfaces is useful in the optimization of crashworthiness and sheet metal forming. In addition, the efficiency of optimization using Space Mapping will be compared to traditional structural optimization using the Response Surface Methodology (RSM). Five examples are used to study the algorithm: one optimization of an analytic function and four structural optimization problems. All examples are constrained optimization problems. In all examples, the algorithm converged to an improved design with all constraints fulfilled, even when a conventional RSM optimization failed to converge. For the crashworthiness design problems, the total computing time for convergence was reduced by 53% using Space Mapping compared to conventional RSM. For the sheet metal forming problems the total computing time was reduced by 63%. The conclusions are that optimization using Space Mapping and surrogate models can be used for optimization in crashworthiness design and sheet metal forming applications with a significant reduction in computing time.

  • 32.
    Kapidzic, Zlatan
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Ansell, Hans
    Saab AB, Linköping, Sweden.
    Conceptual studies of a composite-aluminum hybrid wing box demonstrator2014In: Aerospace Science and Technology, ISSN 1270-9638, E-ISSN 1626-3219, Vol. 32, no 1, p. 42-50Article in journal (Refereed)
    Abstract [en]

    This paper presents a study of two different hybrid composite-aluminum concepts applied to a winglike structure which is exposed to mechanical  and thermal load. The aim of the study is to determine the most suitable  hybrid concept to later on be used in structural fatigue and static testing. In both concepts, the mass is optimized with respect to two different sets of requirements, one of which is currently in use in the fighter aircraft industry and one which is a modified version of the current requirement set. The issues considered in the study are mass, thermal behavior, buckling, bolted joints, failure criteria and fatigue damage, and they are examined in the frame of both requirement sets. The results clearly indicate the order of criticality between the different criteria in the different parts of each concept. Also, the comparison of two requirement sets gives an idea of the degree of influence of the modified criteria on the hybrid concepts and their mass. Based on the mass and the structural behavior in a thermal-mechanical loading one of the hybrid concepts is chosen for further studies and testing.

  • 33.
    Kapidzic, Zlatan
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Ansell, Hans
    Saab AB, Linköping, Sweden.
    Finite element modeling of mechanically fastened composite-aluminum joints in aircraft structures2014In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 109, p. 198-210Article in journal (Refereed)
    Abstract [en]

    A three-dimensional, solid finite element model of a composite-aluminum single-lap bolted joint with a countersunk titanium fastener is developed. The model includes progressive damage behavior of the composite and a plasticity model for the metals. The response to static loading is compared to experimental results from the literature. It is shown that the model predicts the initiation and the development of the damage well, up to failure load. The model is used to evaluate the local force-displacement responses of a number of single-lap joints installed in a hybrid composite-aluminum wing-like structure. A structural model is made where the fasteners are represented by two-node connector elements which are assigned the force-displacement characteristics determined by local models. The behavior of the wing box is simulated for bending and twisting loads applied together with an increased temperature and the distribution of fastener forces and the progressive fastener failure is studied. It is shown that the fastener forces caused by the temperature difference are of significant magnitude and should be taken into account in the design of hybrid aircraft structures. It is concluded that, the account of the non-linear response of the joints results in a less conservative load distribution at ultimate failure load.

  • 34.
    Larsson, Rikard
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Björklund, Oscar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    A study of high strength steels undergoing non-linear strain paths—Experiments and modelling2011In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 211, no 1, p. 121-131Article in journal (Refereed)
    Abstract [en]

    This paper presents an evaluation of the constitutive behaviour, including plastic anisotropy and mixed isotropic-kinematic hardening of two high strength steels, Docol 600DP and Docol 1200M, during strain path changes. A series of tensile and shear tests was performed on both virgin and pre-strained materials. The initial anisotropy and work hardening parameters were obtained from tensile tests, shear tests and a bulge test of the virgin material, whereas the kinematic hardening parameters were identified by comparing numerical predictions to experimental results related to the pre-strained materials. Numerical predictions using the obtained parameters agree well with the experimental results, both in the case of proportional, and under non-proportional strain paths.

  • 35.
    Larsson, Rikard
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    On isotropic-distortional hardeningManuscript (preprint) (Other academic)
    Abstract [en]

    Isotropic-distortional hardening allows for individual stress-plastic strain relations in different straining directions. Such hardening can be obtained by allowing the parameters in the effective stress function to depend on anisotropy functions of the equivalent plastic strain. A methodology to calibrate these anisotropy functions is proposed in this work, and is demonstrated on an austenitic strainless steel. A high exponent eight parameter effective stress function for plane stress states is utilised. The anisotropy functions are calibrated by the use of experimental data from uniaxial tensile test data in three material directions and a balanced biaxial test. The plastic anisotropy is assumed to vary piecewise linearly with respect to the equivalent plastic strain, and it is evaluated at a finite number of plastic strains. Thus, it is correctly represented at each level of plastic strain included in the evaluation, even if large increments in plastic strain are used in the calibration. It was found that there are at least two sets of anisotropy functions which satisfy the conditions in the calibration procedure. The resulting uniaxial stress-strain relations from the two sets of anisotropy functions in four additional straining directions, not included in the calibration set, were compared to the corresponding experimental data. From this validation, one of the anisotropy function sets could be discarded, whereas the other one gave a good prediction of the stress-strain relations in all the four additional directions.

  • 36.
    Larsson, Rikard
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    On the modelling of strain ageing in a metastable austenitic stainless steel2012In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 212, no 1, p. 46-58Article in journal (Refereed)
    Abstract [en]

    The plastic hardening of metastable austenitic stainless steel is partly governed by martensitic transformation, the occurrence of serrated plastic flow, and plastic strain ageing phenomena. In this paper an elasto-viscoplastic material model with isotropic distortional plastic hardening is developed. The model accounts for static and dynamic strain ageing as well as the martensitic transformation. An experimental programme has been conducted in order to fit the model parameters to an austenitic stainless steel within the EN 1.4310 standard. The identification of the dynamic strain ageing was based on so called jump tests, where a sudden strain rate increase was shown to result in an instantaneous positive strain rate sensitivity followed by negative steady state strain rate sensitivity. Furthermore, the static strain ageing was identified by unloading tensile test specimens at specified plastic strains and then reloading these specimens after different periods of time. The observed material behaviour in the test situations can be predicted by the developed model. Lastly, the model was validated by predicting the force-displacement relation of the material in a shear test: the prediction agrees well with experimental results.

  • 37.
    Larsson, Rikard
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Strain rate effects in a high strength dual phase steelManuscript (preprint) (Other academic)
    Abstract [en]

    This work focuses on strain rate effects in a high strength dual phase steel, DP600. Attention is given to the mathematical formulation of the strain rate sensitivity, and to its influence on the strain at localisation. Both an experimental and a numerical study are presented. In the experimental study, uniaxial and notched tensile tests, as well as shear tests were conducted at various loading rates. Furthermore, strain rate jump tests were conducted in order to further investigate the strain rate sensitivity. It is clearly shown that the material has a positive strain rate sensitivity, and that a multiplicative contribution to the flow stress is a better approximation than an additive one. A material model including a non-linear plastic hardening, a high exponent yield surface, a thermal softening effect and a variety of multiplicative strain rate sensitivity functions is presented and calibrated. This material model is used in finite element simulations of the mechanical tests. The predicted results are in good agreement with the experimental findings. The stabilising effect of the strain rate sensitivity is shown to be important whenever strain localisation becomes an issue in finite element simulations. It is also shown that the strain rate sensitivity index depends on the plastic strain rate, which thus is the case also for the stabilising effect. From a supplementary study, it is concluded that the assumed thermal softening will affect the onset of localisation.

  • 38. lI, M. X.D.
    et al.
    Moshfegh, Ramin
    Hållfasthetslära Tekniska fakultetet.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Two-mesh refinement indicators and adaptivity in non-linear explicit finite element analysis of shells using LS-DYNA2000In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, International Journal for Numerical Methods in Biomedical Engineering, ISSN 2040-7939, Vol. 16, no 11, p. 785-800Article in journal (Refereed)
    Abstract [en]

    Two-mesh refinement indicators based on the gradients of effective stresses and effective plastic strains, respectively, are proposed for adaptive finite element analysis of the large deformation, materially non-linear dynamic response of shells. The refinement strategy consists of equi-distributing the variation of stresses or plastic strains over the elements of the mesh. A program module for implementing these refinement indicators has been developed and coupled with the general non-linear finite element explicit code LS-DYNA. Numerical examples including both material and geometric non-linearities are presented. It is shown that these indicators can effectively identify those finite elements, which have high gradients of stresses and strains so that the mesh is refined in the region's undergoing the most severe deformations.

  • 39.
    Lönn, David
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Bergman, Greger
    Gestamp Hardtech AB, Luleå.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Experimental and finite element robustness studies of a bumper system subjected to an offset impact loading2011In: International Journal of Crashworthiness, ISSN 1358-8265, E-ISSN 1754-2111, Vol. 16, no 2, p. 155-168Article in journal (Refereed)
    Abstract [en]

    A product of high quality is a product that performs well, not only in exactly the situations it was designed to handle but also in slightly different situations that arise in the usage of the product. As a specific example, the performance of a bumper system should not depend on small fluctuations in the manufacturing process or on small variations in the impact event. In this work, the robustness of an existing vehicle bumper system subjected to a crash load has been evaluated both experimentally and numerically. In the latter case, different widely used approaches to numerically assess the robustness have been utilised. A reliable numerical robustness study provides the designer with a valuable tool for improving a design, and an evaluation of these methods in this context is therefore of interest. It is concluded that for the example under study, both the Monte Carlo method and the metamodel-based Monte Carlo methods work well. Furthermore, for moderate dispersions levels, i.e. a small design space with no bifurcation in the deformation pattern, a linear response approximation is shown to have a sufficient accuracy to be used in the metamodel-based robustness analysis. The performed numerical robustness studies also point out that the performance of a nominal simulation, i.e. a simulation conducted with mean values for all variables, does not in general predict the mean performance of the finite element model. Finally, some possible design improvements for the bumper system under study are also identified

  • 40.
    Lönn, David
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Fyllingen, Orjan
    Norwegian University of Science and Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Correction: An approach to robust optimization of impact problems using random samples and meta-modelling (vol 37, pg 723, 2010)2010In: International Journal of Impact Engineering, ISSN 0734-743X, E-ISSN 1879-3509, Vol. 37, no 7, p. 878-878Article in journal (Other academic)
    Abstract [en]

    n/a

  • 41.
    Lönn, David
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    Fyllingen, Ørjan
    Norwegian University of Science and Technology, Trondheim.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
    An approach to robust optimization of impact problems using random samples and meta-modelling2010In: International Journal of Impact Engineering, ISSN 0734-743X, E-ISSN 1879-3509, Vol. 37, no 6, p. 723-734Article in journal (Refereed)
    Abstract [en]

    Conventionally optimized structures may show a tendency to be sensitive to variations, for instance in geometry and loading conditions. To avoid this, research has been carried out in the field of robust optimization where variations are taken into account in the optimization process. The overall objective is to create solutions that are optimal both in the sense of mean performance and minimum variability. This work presents an alternative approach to robust optimization, where the robustness of each design is assessed through multiple sampling of the stochastic variables at each design point. Meta-models for the robust optimization are created for both the mean value and the standard deviation of the response. Furthermore, the method is demonstrated on an analytical example and an example of an aluminium extrusion with quadratic cross-section subjected to axial crushing. It works well for the chosen examples and it is concluded that the method is especially well suited for problems with a large number of random variables, since the computational cost is essentially independent of the number of random variables. In addition, the presented approach makes it possible to take into consideration variations that cannot be described with a variable. This is demonstrated in this work by random geometrical perturbations described with the use of Gaussian random fields.

  • 42.
    Lönn, David
    et al.
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Öman, Michael
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Nilsson, Larsgunnar
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Simonsson, Kjell
    Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
    Finite element based robustness study of a truck cab subjected to impact loading2009In: International Journal of Crashworthiness, ISSN 1358-8265, E-ISSN 1754-2111, Vol. 14, no 2, p. 111-124Article in journal (Refereed)
    Abstract [en]

    Optimised designs have a tendency of being sensitive to variations. It is therefore of great importance to analyse this sensitivity to assure that a design is robust, i.e. sufficiently insensitive to variations. To analyse robustness, variations are introduced in model parameters and their influences on simulation responses are studied. This is usually achieved using the Monte Carlo method. Though, due to the large number of simulations needed, the Monte Carlo method is very costly for problems requiring a long computing time. Therefore, in this work a meta model-based Monte Carlo method is used to evaluate the robustness of a vehicle structure. That is, the Monte Carlo analysis is performed on a surface approximation of the true response, over the domain of interest. The methodology used is to first identify the variables that influence the response the most, referred to as a screening, using simple linear response surfaces. This is followed by a more detailed sensitivity analysis using only the identified variables and a quadratic response surface, thereby incorporating second order effects. A truck cab model exposed to a pendulum impact load is used as an evaluation of this method, and the important variables and their influence on the response are identified. The effect of including results from forming simulations is also evaluated using the truck cab model. Variations are introduced before forming simulations, thereby taking forming effects into account in the sensitivity analysis. The method was found to be a good tool to identify important dispersion variables and to give an approximate result of the total dispersion, all with a reasonable amount of simulations.

  • 43.
    Marklund, Per-Olof
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
    Optimization of a car body component subjected to side impact2001In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 21, no 5, p. 383-392Article in journal (Refereed)
    Abstract [en]

    This paper explores structural optimization methods applied to a car side impact. The use of local and global approximation methods has been compared, resulting in a recommendation that global approximation methods should be used for this kind of transient loading problems. The numerical simulations have been carried out using the explicit finite element program LS-DYNA. The problem studied is the weight minimization of the B-pillar, situated between the front and the rear door of the car, without compromising the safety of the car occupants. All results are related to the original B-pillar in the SAAB 95 car. By using global approximations in the form of linear and quadratic response surfaces it is shown that the weight of the B-pillar can be reduced by 25% without the loss of safety.

  • 44.
    Marklund, Per-Olof
    et al.
    Linköping University, Department of Mechanical Engineering.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Optimization of a Car Body Component Subjected to Side Impact2000In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488Article in journal (Other academic)
  • 45.
    Marklund, Per-Olof
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
    Simulation of airbag inflation processes using a coupled fluid structure approach2002In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 29, no 4-5, p. 289-297Article in journal (Refereed)
    Abstract [en]

    This paper explores simulation techniques for airbag inflation problems using a coupled fluid structure approach. It is to be seen as an initial study on the phenomena occurring in an airbag during a so called out of position occupant impact. The problem studied in this paper is an airbag which is set to impact a head form. The head form is positioned at a very short distance from the airbag. A multi material arbitrary Lagrangian Eulerian technique in the explicit finite element code LS-DYNA is used for the fluid and it is coupled to the structure using a penalty based fluid structure contact algorithm. The results for the head form acceleration and velocity show a good agreement to experimentally obtained values. At the early stages of the inflation process a high pressure zone is found to develop between the gas inlet and the head form. Consequently the pressure difference between the inlet and the high pressure zone is too low for an a priori assumption of sonic flow at the inlet, which is a common requirement in the control volume models used in the industry today.

  • 46.
    Marklund, P.-O.
    et al.
    Engineering Research, Garnisonen, Brigadgatan 16, SE-58131 Limköping, Sweden.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
    Optimization of airbag inflation parameters for the minimization of out of position occupant injury2003In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 31, no 6, p. 496-504Article in journal (Refereed)
    Abstract [en]

    In this paper optimization techniques together with coupled fluid-structure analysis are used to provide a better understanding of the interaction between the airbag inflation process and an Out Of Position occupant. We provide a concept for, and exemplify how these techniques can be applied to optimize the airbag inflator characteristics in order to minimize occupant injury. For a simplified, but realistic, problem we show that the head acceleration can be reduced by approximately 65% by optimizing the inlet characteristics.

  • 47. Martikka, H.I.
    et al.
    Varis, J.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Clinch joint test simulation and optimum design2000In: Welding Conference LUT Join99,1999, 2000Conference paper (Other academic)
  • 48.
    Moshfegh, R.
    et al.
    Ind Res & Dev Corp, IVF, Proc Dev, SE-43153 Molndal, Sweden.
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
    Larsson, M.
    Saab Automobile AB, SE-46180 Trollhattan, Sweden.
    Estimation of process parameter variations in a pre-defined process window using a Latin hypercube method2008In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 35, no 6, p. 587-600Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to present a methodology that provides an analytical tool for estimation of robustness and response variation within a pre-defined process window. To exemplify the developed methodology, the stochastic simulation technique is used for a sheet-metal forming application. A sampling plan based on the Latin hypercube sampling method for variation of design parameters is utilized, and the thickness reduction is specified as the response. Moreover, the response surface methodology is applied for understanding the quantitative relationship between design parameters and response value. The conclusions of this study are that the applied method gives a possibility to illustrate and interpret the variation of the response versus a design parameter variation. Consequently, it gives significant insights into the usefulness of individual design parameters. It has been shown that the method enables us to estimate the admissible design parameter variations and to predict the actual safe margin for given process parameters. Furthermore, the dominating design parameters can be predicated using sensitivity analysis, and this in its turn clarifies how the reliability criteria are met. Finally, the developed software can be used as an additional module for set-up of stochastic finite element simulations and to collect the numerical results from different solvers within different applications.

  • 49.
    Moshfegh, Ramin
    et al.
    Teknika fakultetet Hållfasthetslära.
    Li, Xiangdong
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Adaptive Finite Element Simulation of Sheet Metal Forming Process Using Gradient Based Indicators2001In: 6th International LS-DYNA Users Conference 2000,2000, Detroit, Michigan, USA: LSDYNA , 2001Conference paper (Other academic)
  • 50.
    Moshfegh, Ramin
    et al.
    Hållfasthetslära Tekniska fakultetet.
    Li, Xiangdong
    Nilsson, Larsgunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Solid Mechanics.
    Gradient-based refinement indicators in adaptive finite element analysis with special reference to sheet metal forming2000In: Engineering computations, ISSN 0264-4401, E-ISSN 1758-7077, Vol. 17, no 8, p. 910-932Article in journal (Refereed)
    Abstract [en]

    Two mesh refinement indicators based on the gradients of effective stress (GSIG) and effective plastic strain (GEPS), respectively, are proposed for adaptive finite element analysis of the large deformation, quasi-static or dynamic response of shell structures. The mesh refinement indicators are based on equi-distributing the variation of stresses or plastic strains over the elements of the mesh. A program module is developed and implemented in the non-linear explicit finite element code LS-DYNA. This module provides element-wise refinement evaluations so that selective mesh refinements are carried out in regions of the mesh where the values of local indicators exceed a user-specified tolerance. The FE model of a conventional deep drawing process is used as a numerical model, including both material and geometrical non-linearities, in order to demonstrate the versatility of the two refinement indicators. Four different refinement indicators, based on angle change, thickness change, GSIG and GEPS, are applied in this investigation. The numerical results are compared with experimental results regarding the thickness distribution versus cup height, cup height variation versus circumference angle, effective plastic strain in the deformed sheet and punch force. It is shown that the proposed indicators can identify finite elements which have high gradients of effective stress or effective plastic strain so that the mesh is refined in the regions undergoing the most severe deformations and the numerical results are improved.

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