Novel finite element algorithms with applications to skeletal muscle simulation

This thesis develops a musculoskeletal simulation framework and showcases the algorithmic developments that arose in the process of creating it. Muscles are simulated as deformable Lagrangian solids with a transversely isotropic, quasi-incompressible constitutive model coupled to articulated rigid bones in the skeleton. Muscle and bone geometry is created from the visible human data set using an implicit surface based tetrahedral meshing algorithm for creating meshes that are well suited for large deformation. Additionally, a novel invertible finite element algorithm (IFEM) designed specifically for largely deforming skeletal muscles is presented. Typical finite element based simulations of elastic solids fail when the interpolating functions misinterpret large deformations as having locally negative volume at quadrature points, our approach extends the elastic response in a meaningful way to such configurations, drastically improving robustness to large deformation. Simulations are done with semi-implicit Newmark integration and quasistatic time stepping schemes. In the case of the latter, we present a novel quasistatic algorithm that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration. Quasistatic and implicit time integration schemes are typically employed to alleviate the stringent time step restrictions imposed by their explicit counterparts. However, time step restrictions can also be ameliorated with regular mesh elements. As a result, we present a muscle geometry embedding framework that alleviates time step restrictions by virtue of this principle. A fascia/collision algorithm is also presented in the context of this embedding framework. Finally, though all musculoskeletal simulations in this thesis make use of kinematically prescribed skeletal motion, we would ultimately like to simulate the skeleton as a dynamic articulated rigid body. We present a preliminary step in this direction with a prestabilization framework for enforcing articulation constraints.