Coupling transport equations to mechanics in the material point method using an approximate full capacity matrix inverse

Abstract

Coupling solutions of one or more transport equations to mechanics modeling in the material point method (MPM), extends MPM to a platform for solving multi-physics problems. Unfortunately, the standard MPM approach to transport equations using a lumped transport capacity matrix is prone to large oscillations in particle values especially near interfaces, cracks, or rapid changes in transport value. Switching from lumped capacity matrix methods to an approximate full capacity matrix approach can eliminate those oscillations. Although this switch can cause unwanted numerical diffusion, that problem can be suppressed using periodic or blending options. Several examples illustrate the new methods for heat conduction, solvent transport, poroelasticity, and phase field fracture simulations. In thermal calculations, the new methods improve accuracy for tracking thermodynamics state functions.