Numerical Methods and Analysis Tools for Material Mechanics Across Scales

Abstract

A material's structures at different lengthscales profoundly impact the material's properties and performance. Therefore, it is necessary to investigate material mechanics across scales to develop useful engineering applications. This thesis presents the developments of a few analysis tools and numerical methods aiding the study of material mechanics across scales.

We start with developing computational geometry software libraries that leverage modern computing power and incorporate multi-threaded parallel computation. Firstly, we developed a multi-threaded version of Voro++, a software library to generate Voronoi diagrams for a set of particles. Multi-threaded Voro++ enables the analysis of large-scale particle systems, aiding with research in understanding microstructures of materials. We further extended our research to address challenges in meshing for finite element (FEM) computations, which are often used in macroscopic continuum simulation of materials. We use the multi-threaded Voro++ to develop TriMe++, a multi-threaded triangle meshing software for 2D shapes. TriMe++ can aid with large-scale FEM simulations.

We then switch the focus to continuum modeling of materials at the macroscopic level. We investigated the plastic deformation of elastoplastic materials in the quasi-static limit. The existing numerical method to solve quasi-static elastoplasticity is a projection method analogous to Chorin's projection method (1968) for incompressible Newtonian fluids. We developed a few numerical improvements to the existing projection method, including (1) a second-order temporal formulation; (2) a FEM implementation of the projection step; (3) an efficient adaptive time-stepping scheme. The improvements can aid with efficient and accurate simulations of the plastic deformation of quasi-static elastoplastic materials in different loading scenarios.