Multi-physics computational dynamics using complementarity and hybrid lagrangian-eulerian methods

This thesis proposes a novel formulation for modeling and simulating (a) rigid and deformable bodies; (b) soft materials, which exhibit mixed elastic and plastic behavior; and, (c) fluids, in a single coherent framework using a constraint based formulation. Each of these materials exists in a variational framework where rigid bodies interact through frictional contact, deformable objects are simulated as tetrahedral elements with a volumetric strain constraint, and fluids are modeled using a many body density constraint. Boundary conditions are handled through frictional contacts that enforce non-penetration. Soft, elasto-plastic materials are handled using the Material Point Method (MPM), which is coupled to the variational framework using a Chorin style splitting technique on the stress tensor to separate the deviatoric and dilational components. The deviatoric component is solved using a semi-implicit treatment of the MPM method which models the internal friction of the material.;Two different approaches for solving the dilational component, which models expansion/contraction of the material, are presented and coupled using frictional contact constraints to rigid and deformable bodies. The first approach leverages frictionless rigid spheres with compliant cohesive contact as an approximation for the dilational component of elastic compressible material. The second extends the constraint fluid framework and uses a Lagrangian pressure solve to model fluid that can handle the full spectrum of compressible and incompressible material. This mixed treatment of deviatoric and dilational stresses/strains ultimately allows for large timesteps while simulating extremely complex material behavior as demonstrated through the examples in this document.