# Coordinate transformation methodology for simulating quasi-static elastoplastic solids

## TL;DR

This paper introduces a coordinate transformation method for simulating quasi-static elastoplastic solids, enabling precise comparison between molecular dynamics and continuum mechanics through a fixed grid framework.

## Contribution

It develops a novel projection-based simulation framework with coordinate transformations to accurately model quasistatic elastoplastic deformation.

## Key findings

- Effective simulation of shear band evolution in metallic glasses.
- Comparison of shear and pure shear conditions on deformation.
- Validation of the coordinate transformation approach.

## Abstract

Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypoelastoplastic mechanical model, and develop a projection method to enforce quasistatic equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and which imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.