Dynamically Enriched MPM for Invertible Elasticity

Abstract

We extend the material point method (MPM) for robust simulation of extremely large elastic deformation. This facilitates the application of MPM towards a unified solver since its versatility has been demonstrated lately with simulation of varied materials. Extending MPM for invertible elasticity requires accounting for several of its inherent limitations. MPM as a meshless method exhibits numerical fracture in large tensile deformations. We eliminate it by augmenting particles with connected material domains. Besides, constant redefinition of the interpolating functions between particles and grid introduces accumulated error which behaves like artificial plasticity. We address this problem by utilizing the Lagrangian particle domains as enriched degrees of freedom for simulation. The enrichment is applied dynamically during simulation via an error metric based on local deformation of particles. Lastly, we novelly reformulate the computation in reference configuration and investigate inversion handling techniques to ensure the robustness of our method in regime of degenerated configurations. The power and robustness of our method are demonstrated with various simulations that involve extreme deformations. We extend the material point method (MPM) for robust simulation of extremely large elastic deformation. This facilitates the application ofMPMtowards a unified solver since its versatility has been demonstrated lately with simulation of variedmaterials. Extending MPM for invertible elasticity requires accounting for several of its inherent limitations. MPM as a meshless method exhibits numerical fracture in large tensile deformations. We eliminate it by augmenting particles with connected material domains. Besides, constant redefinition of the interpolating functions between particles and grid introduces accumulated error which behaves like artificial plasticity. We address this problem by utilizing the Lagrangian particle domains as enriched degrees of freedom for simulation. We also novelly reformulate the computation in reference configuration and investigate inversion handling techniques to ensure the robustness of our method in regime of degenerated configurations