A Novel Framework for GPU-Parallelized Peridynamics with Applications in Nonlinear Elasticity and Topology Optimization

Abstract

This work focuses on advancing the state-of-the-art of the peridynamic simulation method. Peridynamics is a framework for modelling continuum mechanics, similar to the finite element method (FEM). The peridynamic formulation, which involves a meshfree discretization of a continuum into material points and evaluation of force-exerting interactions between these points, allows representation of complex physical phenomena such as nonlinear mechanics, crack propagation, and material failure more naturally than gradient-based approaches like FEM. This work presents a three-pronged approach towards advancing the state-of-the-art of peridynamic simulation: Chapter 2 definitively improves treatment of the long-standing "peridynamic surface effect", which limits the theoretical accuracy of the peridynamic method due to the method's formulation assuming all material points to be in the bulk of the body. The solution developed here extends an approach which eliminates the effect in simple geometries to apply a specialized boundary treatment to arbitrary domain shapes. Chapter 3 develops a novel, high performance software package for parallelized peridynamic simulation on graphics processing units (GPUs). This approach is several hundred times faster than equivalent serial approaches, and several times faster than alternative GPU-based approaches recently developed by other researchers. Additionally, this software is capable of simulating problem sizes an order of magnitude larger than competing methods on limited GPU memory. Finally, Chapter 4 applies this highly-efficient software towards novel applications of peridynamics, particularly in nonlinear structural analysis and large scale topology optimization. Specifically, the GPU peridynamic framework is capable of evaluating large deformations 2-3 orders of magnitude faster than state-of-the-art nonlinear FEM solvers. The framework is demonstrated to produce accurate simulations of behavior in auxetic structures exhibiting geometric discontinuities and nonlinear deformations, a use case which demands nonlinear solution for reasonable results; the peridynamic solver runs 1250x faster than the GPU-accelerated commercial software ANSYS. Finally, utilizing the GPU framework for the structural analysis step of large-scale topology optimization problems produces optimal topologies 35-65x faster than state-of-the-art FEM optimizers run on the CPU, and 2-4x faster than GPU-based FEM optimizers running on identical hardware.