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Theory of Residual Stresses with Application to an Arterial Geometry
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-8460-0131
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.
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.

Place, publisher, year, edition, pages
2007. Vol. 59, no 4-5, 341-364 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-14330OAI: oai:DiVA.org:liu-14330DiVA: diva2:23257
Available from: 2007-03-16 Created: 2007-03-16 Last updated: 2017-05-15
In thesis
1. Soft Tissue Mechanics with Emphasis on Residual Stress Modeling
Open this publication in new window or tab >>Soft Tissue Mechanics with Emphasis on Residual Stress Modeling
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
Mechanics, Residual Stress, Growth, Remodeling
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-8490 (URN)978-91-85715-50-3 (ISBN)
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

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Klarbring, AndersOlsson, TobiasStålhand, Jonas

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