Mixed finite elements for thermoelastic modeling of biological matter

In this presentation we look at various finite element methods for modeling biological matter. Because biological matter is nearly incompressible, volumetric locking must be accounted for. Mixed finite elements are known to overcome locking and in addition are particularly suited for problems where a high-order polynomial representation of the stress tensor is desirable. This is in contrast to the majority of commercial software which only allows for piecewise constant approximations of the stress tensor. We present a general mixed finite element framework that is capable of handling thermoelastic, poroelastic, and viscoelastic models of biological matter in the small displacement regime.