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Soft Tissue Mechanics with Emphasis on Residual Stress Modeling
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns residual stress modeling in soft living tissues. The word living means that the tissue interacts with surrounding organs and that it can change its internal properties to optimize its function. From the first day all tissues are under pressure, due, for example, to gravity, other surrounding organs that utilize pressure on the specific tissue, and the pressure from the blood that circulates within the body. This means that all organs grow and change properties under load, and an unloaded configuration is never present within the body. When a tissue is removed from the body, the obtained unloaded state is not naturally stress free. This stress within an unloaded body is called residual stress. It is believed that the residual stress helps the tissue to optimize its function by homogenizing the transmural stress distribution.

The thesis is composed of two parts: in the first part an introduction to soft tissues and basic modeling is given and the second part consist of a collection of five manuscripts. The first four papers show how residual stress can be modeled. We also derive evolution equation for growth and remodeling and show how residual stress develops under constant pressure. The fifth paper deals with damage and viscosity in soft tissues.

Place, publisher, year, edition, pages
Institutionen för konstruktions- och produktionsteknik , 2007. , 27 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1081
Keyword [en]
Mechanics, Residual Stress, Growth, Remodeling
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:liu:diva-8490ISBN: 978-91-85715-50-3 (print)OAI: oai:DiVA.org:liu-8490DiVA: diva2:23261
Public defence
2007-04-13, Sal C3, Hus C, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-05-15
List of papers
1. On Compatible Strain with Reference to Biomechanics
Open this publication in new window or tab >>On Compatible Strain with Reference to Biomechanics
2005 (English)In: Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267, Vol. 85, no 6, 440-448 p.Article in journal (Refereed) Published
Abstract [en]

In previous studies, residual stresses and strains in soft tissues have been experimentally investigated by cutting the material into pieces that are assumed to become stress free. The present paper gives a theoretical basis for such a procedure, based on a classical theorem of continuum mechanics. As applications of the theory we study rotationally symmetric cylinders and spheres. A computer algebra system is used to state and solve differential equations that define compatible strain distributions. A mapping previously used in constructing a mathematical theory for the mechanical behavior of arteries is recovered as a corollary of the theory, but is found not to be unique. It is also found, for a certain residual strain distribution, that a sphere can be cut from pole to pole to form a stress and strain free configuration.

Keyword
biomechanics, compatible strain, curvature tensor, elasticity, residual stress, soft tissue
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14329 (URN)10.1002/zamm.200410192 (DOI)
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-05-15
2. Theory of Residual Stresses with Application to an Arterial Geometry
Open this publication in new window or tab >>Theory of Residual Stresses with Application to an Arterial Geometry
2007 (English)In: Archives of Mechanics, ISSN 0373-2029, Vol. 59, no 4-5, 341-364 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents a theory of residual stresses, with applications to biomechanics, especially to arteries. For a hyperelastic material, we use an initial local deformation tensor K as a descriptor of residual strain. This tensor, in general, is not the gradient of a global deformation, and a stress-free reference configuration, denoted B¯, therefore, becomes incompatible. Any compatible reference configuration B0 will, in general, be residually stressed. However, when a certain curvature tensor vanishes, there actually exists a compatible and stress-free configuration, and we show that the traditional treatment of residual stresses in arteries, using the opening–angle method, relates to such a situation.

Boundary value problems of nonlinear elasticity are preferably formulated on a fixed integration domain. For residually stressed bodies, three such formulations naturally appear: (i) a formulation relating to B0 with a non-Euclidean metric structure; (ii) a formulation relating to B0 with a Euclidean metric structure; and (iii) a formulation relating to the incompatible configuration B¯. We state these formulations, show that (i) and (ii) coincide in the incompressible case, and that an extra term appears in a formulation on B¯, due to the incompatibility.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14330 (URN)
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-05-15
3. Modeling initial strain distribution in soft tissues with application to arteries
Open this publication in new window or tab >>Modeling initial strain distribution in soft tissues with application to arteries
2006 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 5, no 1, 27-38 p.Article in journal (Refereed) Published
Abstract [en]

A general theory for computing and identifying the stress field in a residually stressed tissue is presented in this paper. The theory is based on the assumption that a stress free state is obtained by letting each point deform independently of its adjacent points. This local unloading represents an initial strain, and can be described by a tangent map. When experimental data is at hand in a specific situation, the initial strain field may be identified by stating a nonlinear minimization problem where this data is fitted to its corresponding model response. To illustrate the potential of such a method for identifying initial strain fields, the application to an in vivo pressure–radius measurement for a human aorta is presented. The result shows that the initial strain is inconsistent with the strain obtained with the opening-angle-method. This indicates that the opening-angle-method has a too restrictive residual strain parameterization, in this case.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14331 (URN)10.1007/s10237-005-0008-8 (DOI)
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-12-13
4. Residual Stresses in Soft Tissues as a Consequence of Growth and Remodeling: application to an arterial geometr
Open this publication in new window or tab >>Residual Stresses in Soft Tissues as a Consequence of Growth and Remodeling: application to an arterial geometr
2008 (English)In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 27, no 6, 959-974 p.Article in journal (Refereed) Published
Abstract [en]

We develop a thermodynamically consistent model for growth and remodeling in elastic arteries. The model is specialized to a cylindrical geometry, strain energy of the Holzapfel–Gasser–Ogden type and remodeling of the collagen fiber angle. A numerical method for calculating the evolution of the adaptation process is developed. For a particular choice of the thermodynamic forces of growth and remodeling (configurational forces), it is shown that an almost homogeneous transmural axial and tangential stress distribution is obtained. Residual stresses develop during this adaption process and these resemble what is found in experiments and by parameter identification methods.

Keyword
Configurational forces, Growth, Remodeling, Residual stress, Artery
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14332 (URN)10.1016/j.euromechsol.2007.12.006 (DOI)
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-12-13
5. Modeling of Passive Behavior of Soft Tissues Including Viscosity and Damage
Open this publication in new window or tab >>Modeling of Passive Behavior of Soft Tissues Including Viscosity and Damage
2006 (English)In: III European Conference on Computational Mechanics, Lisbon, 5–9 June, 2006, 191-191 p.Conference paper, Published paper (Refereed)
Abstract [en]

The mechanical properties of soft tissues depend strongly on the orientation of their fibers, and usually they have a highly nonlinear behavior: their stiffness increases as they are stretched. We are interested here in the passive behavior of soft tissues, when subjected to significant stretches, possibly leading to damage. In this paper we develop a model for a transversely isotropic material that has a damageable viscoelastic behavior. This model is then used to simulate the damage evolution of the tissue. The model is developed with the underlying framework of hyperelasticity, and the corresponding strain energy has different parts associated to different contributions to the material behavior: volumetric, isotropic, anisotropic and dissipative contributions. Since soft tissues are almost incompressible we use a multiplicative split of the deformation gradient into a volume preserving part and a part with (small) volume changes. The anisotropic behavior is characterized by the existence of a family of fiber directions within the tissue. The viscoelastic behavior associated with the non-equilibrium stress is treated as a standard solid material with M Maxwell elements simulating the fact that the response of soft tissues is almost independent of the loading frequency. The total damage is modeled by splitting the energy degradation into one isotropic part and one anisotropic part. That is, we can have fiber degradation independently of the damage of the surrounding matrix. The model is implemented in the commercial Finite element software ABAQUS and the tissue behavior is described by an user subroutine (UMAT). Qualitative features of the model are illustrated and discussed.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14333 (URN)10.1007/1-4020-5370-3_191 (DOI)978-1-4020-4994-1 (ISBN)
Available from: 2007-03-16 Created: 2007-03-16

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