EU Regional School - Holzapfel Seminar
Prof. Dr. Gerhard Holzapfel - Models for Fiber-Reinforced Elastic Solids with a Focus on Soft Biological Tissues
Institute of Biomechanics, Graz University of Technology, Austria
This short course provides a summary of models for fiber-reinforced elastic solids with distributed fiber orientations. As a motivation we start with a simple 1D problem which we then develop further to 3D considering a 3D isotropic fiber dispersion, perfectly aligned fibers, a rotationally symmetric dispersion and a non-rotationally symmetric dispersion. We review basic elements from the nonlinear theory of continuum mechanics that is required in the modeling of fiber-reinforced elastic solids. Of particular relevance are the structure tensors and related deformation invariants required to consider fibers and their dispersed directions in constitutive models. We also provide computational aspects needed for finite element implementation of the discussed models, and focus on an efficient formulation which avoids non-physical responses in the numerical analysis of anisotropic materials. The effect of the fiber structure on the material response is discussed on the basis of several examples. We discuss changes of the fiber structure in images obtained from cardiovascular tissues in health and disease using high-resolution optical microscopy. Related finite-element simulations highlight the need to incorporate the structural differences of soft biological (fibrous) tissues.