A simple history dependent remeshing technique to increase finite element model stability in elastic surface deformations

TL;DR

This paper introduces a straightforward adaptive remeshing method that enhances the stability and accuracy of finite element simulations of elastic surface deformations by effectively transferring history-dependent variables during mesh updates.

Contribution

It presents a novel, easy-to-implement surface remeshing technique that preserves initial configuration and history variables, improving simulation stability and reducing errors.

Findings

Reduces mesh distortion errors in simulations

Increases stability of finite element models during large deformations

Eases implementation of remeshing in elastic surface deformation simulations

Abstract

In this paper, we present and validate a simple adaptive surface remeshing technique to transfer history dependent variables from an old distorting mesh to a new mesh during finite element simulations of elastic surface deformation. This technique allows us to reduce the error arising from excessive mesh distortion whilst preserving information about the initial configuration of the mesh and the history dependent variables. The transfer technique presented here constructs the initial configuration of the new mesh by considering the distortion incurred by the elements of the old mesh and projecting backward in time. Using this new initial configuration, the stress and strain over the new mesh can be easily calculated. After presenting the necessary steps to reconstruct the initial configuration, we show that this relatively simple transfer technique adds stability to finite element simulations and reduces the spatial error and the strain error across the domain. The novel transfer technique presented in this paper is easy to implement and provides a simple strategy to add stability to simulations undergoing large deformations.