Integrating Peridynamics with Material Point Method for Elastoplastic Material Modeling

Abstract

We present a novel integral-based Material Point Method (MPM) using state based peridynamics structure for modeling elastoplastic material and fracture animation. Previous partial derivative based MPM studies face challenges of underlying instability issues of particle distribution and the complexity of modeling discontinuities. To alleviate these problems, we integrate the strain metric in the basic elastic constitutive model by using material point truss structure, which outweighs differential-based methods in both accuracy and stability. To model plasticity, we incorporate our constitutive model with deviatoric flow theory and a simple yield function. It is straightforward to handle the problem of cracking in our hybrid framework. Our method adopts two time integration ways to update crack interface and fracture inner parts, which overcome the unnecessary grid duplication. Our work can create a wide range of material phenomenon including elasticity, plasticity, and fracture. Our framework provides an attractive method for producing elastoplastic materials and fracture with visual realism and high stability.

A Lagrangian Particle‐based Formulation for Coupled Simulation of Fracture and Diffusion in Thin Membranes

“…This integral formulation for continuum mechanics has also been introduced in computer graphics for simulations of deformable objects with fracture. Current research [CZZ*18, LZC*19, HWW17] has so far focused on peridynamics formulations for volumetirc objects and produced persuasive effects. However, a peridynamics formulation for membrane structures, which is surface‐based, as well as its coupling with diffusion, remains unclear in graphics.…”

“…The governing equations of motion in peridynamics are spatial integral equations instead of PDEs. The peridynamics model has been recently investigated in computer graphics [LBC*14, CZZ*18, LZC*19, HWW17] for simulating fracture in volumetric deformable objects.…”

Integral-Based Material Point Method and Peridynamics Model for Animating Elastoplastic Material

“…A preliminary version of this work has been reported which created the innovative MPM with peridynamics truss particle structure for modeling several kinds of elastoplastic objects [15]. This work continues to investigate the concept of integrating the deformation displacement and simulation the response, while introducing the linearized peridynamics theory to create more general effects, such as viscoelastic solids and fluids.…”