Virtual elements on agglomerated finite elements to increase the critical time step in elastodynamic simulations

TL;DR

This paper explores how virtual elements on agglomerated finite elements can enhance the critical time step in elastodynamic simulations, especially on meshes with poor element quality, leading to faster explicit dynamic computations.

Contribution

It introduces a method using virtual elements on agglomerated polyhedra to improve critical time step estimates in poor-quality meshes for elastodynamic simulations.

Findings

Critical time step becomes insensitive to mesh quality with agglomerated virtual elements.

Significant reduction in solution time demonstrated on a tapered beam simulation.

VEM on agglomerated elements maintains stability on poorly-shaped meshes.

Abstract

In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE) simulations. Low-quality finite elements are common when meshing realistic complex components, and while tetrahedral meshing technology is generally robust, meshing algorithms cannot guarantee high-quality meshes for arbitrary geometries or for non-water-tight computer-aided design models. For reliable simulations on such meshes, we consider FE meshes with tetrahedral and prismatic elements that have badly-shaped elements$-$tetrahedra with dihedral angles close to $0^\circ$ and $180^\circ$, and slender prisms with triangular faces that have short edges$-$and agglomerate such `bad' elements with neighboring elements to form a larger polyhedral virtual element. On each element, the element-eigenvalue inequality is used to estimate the critical time step. For a suite of illustrative finite element meshes with $\epsilon$ being a mesh-coordinate parameter that leads to poor mesh quality, we show that adopting VEM on the agglomerated polyhedra yield critical time steps that are insensitive as $\epsilon \rightarrow 0$. The significant reduction in solution time on meshes with agglomerated virtual elements vis-$\`a$-vis tetrahedral meshes is demonstrated through explicit dynamics simulations on a tapered beam.