Meshless Methods for Large Deformation Elastodynamics

TL;DR

This paper reviews meshless methods for simulating large deformation elastodynamics, highlighting their advantages over mesh-based methods and addressing numerical challenges, with a focus on benchmarking and reproducibility.

Contribution

It provides a comprehensive benchmark of various meshless methods for large deformation elastodynamics, including publicly available source code for reproducibility.

Findings

Meshless methods can handle larger deformations than FEM.

Numerical issues like zero energy modes and tensile instability are significant.

Benchmarking reveals strengths and limitations of different meshless approaches.

Abstract

Meshless methods are a promising candidate to reliably simulate materials undergoing large deformations. Unlike mesh based methods like the FEM, meshless methods are not limited in the amount of deformation they can reproduce since there are no mesh regularity constraints to consider. However, other numerical issues like zero energy modes, the tensile instability and disorder of the discretization points due to the deformation may impose limits on the deformations possible. It is thus worthwhile to benchmark a wide array of these methods since a proper review to this end has been missing from the literature so far. In the interest of reproducibility, the complete source code of all methods considered is made public.