Finite Volume Methods for the Simulation of Skeletal Muscle

Abstract

Since it relies on a geometrical rather than a variational framework, many find the finite volume method (FVM) more intuitive than the finite element method (FEM).We show that the FVM allows one to interpret the stress inside a tetrahedron as a simple 'multidimensional force' pushing on each face. Moreover, this interpretation leads to a heuristic method for calculating the force on each node, which is as simple to implement and comprehend as masses and springs. In the finite volume spirit, we also present a geometric rather than interpolating function definition of strain. We use the FVM and a quasi-incompressible, transversely isotropic, hyperelastic constitutive model to simulate contracting muscle tissue. B-spline solids are used to model fiber directions, and the muscle activation levels are derived from key frame animations.