Simbios Talk by Alex Ten Eyck, Stanford University, November 12, 2008

Title: Developments in Finite Element Methods for Simulation of Biological Tissues

The mechanics of biological tissues such as muscle, blood vessel, and cartilage are commonly studied with finite element analysis. A common challenge for finite element analysis is accurately calculating the stresses while preserving the incompressible material behavior of biological tissue. Enhanced strain, mixed methods, reduced integration, and more recently discontinuous Galerkin are some of the finite element methods capable of accurately predicting the mechanical behavior of incompressible materials. During this Simbios talk I will present the blood vessel micromechanics library on which uses a parallel discontinuous Galerkin implementation to study the micromechanics of blood vessel tissue. Although discontinuous Galerkin has been shown to be a highly accurate and robust method, a more commonly employed method for the study of biological tissue is the enhanced strain method. The enhanced strain method, like discontinuous Galerkin and mixed methods, may display numerical instabilities when approximating the solutions to nonlinear elasticity problems. Borrowing from the stabilization techniques we developed for discontinuous Galerkin, we have successfully developed a stable class of enhanced strain methods for nonlinear elasticity problems. In this talk I will give a brief overview of enhanced strain, the instabilities that arise in nonlinear elasticity problems, and the stable class of enhanced strain methods.