Towards a stable and fast dynamic skeletal muscle model

Forward simulations of three-dimensional, continuum-mechanical skeletal muscle models are computationally demanding and expensive. To adequately represent the muscles’ mechanical behaviour, a fully dynamic modelling framework based on the theory of finite hyperelasticity, which accounts for the highly nonlinear, anisotropic, viscoelastic and incompressible material behaviour, needs to be established. Discretisation of the governing equations yields a nonlinear second-order differential algebraic equation (DAE) system, which represents a challenge for solution strategies as well as for the application of model order reduction techniques. In this contribution, we will compare different solution strategies (DAE index reduction, different solvers) as well as the performance of reduced order models obtained by means of Galerkin and Petrov-Galerkin projection using different projection and test spaces.