An Efficient and Accurate Integrator for Nearly- and Fully-Incompressible Nonlinear Elastodynamics

Scientific fields like biomedical engineering and predictive medicine depend on the accurate resolution of dynamics in incompressible elastic solids. The numerical stiffness inherent to incompressible dynamics precludes explicit time integrators from being utilized in these contexts, but implicit methods are comparatively computationally expensive. This dissertation introduces a novel semi-implicit time integration scheme based on the second order backward differentiation formula for the resolution of nonlinear Lagrangian dynamics in nearly- and fully-incompressible hyperelastic solids. The topic of temporal accuracy in semi-implicit integration schemes has not been rigorously discussed, particularly in application to nonlinear dynamics. The accuracy and stability properties of this solver will be explored and computationally verified. Furthermore, weaknesses in the presented scheme will be highlighted and addressed through the introduction of two related integrators. Finally, the potential application of this solver in the context of fluid-structure interaction via distributed Lagrange multiplier methods will be presented.