Modeling Residual Stress Fields in Soft Tissues : with Application to Human Arteries

Sammanfattning: Biomechanics or Mechanics of Biology comprises many different fields. This thesis deals with soft tissues or living tissues and the fact that these materials live in a pressurized environment. This means that an unloaded tissue may not be stress free. The stress in an unloaded body is usually called residual stress. This thesis consist of an introduction to continuum mechanics and to soft tissues, and three research papers.The first paper deals with a zero stress configuration and the question of compatibility. It is shown that the zero stress configuration not necessarily constitutes a compatible body. The condition for compatibility is analyzed and exemplified on a cylinder and a sphere.In the second paper a model for residually stressed arteries based on local deformations is developed. The material properties for a human aorta is identified by the solution to an optimization problem. The resulting initial strains show a non constant behavior and this behavior cannot be described by the commonly used opening- angle model.The last paper is about formulating boundary value problems for initially stressed bodies in three different reference configurations. Firstly, the equilibrium equation and constitutive relation are stated on the unloaded residually stressed body. Secondly, all material points are relieved from stress by a tangent map and the new stress free configuration, which may be incompatible, is used to state the boundary value problem. Thirdly; we use the relieving tangent map to induce a new metric on the body. This induced metric is in general non Euclidean. Finally, we formulate the boundary value problem on this manifold.