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In this paper, we use the first-order virtual element method (VEM) toinvestigate the effect of shape quality of polyhedra in the estimation of thecritical time step for explicit three-dimensional elastodynamic finite element(FE) simulations. Low-quality finite elements are common when meshing realisticcomplex components, and while tetrahedral meshing technology is generallyrobust, meshing algorithms cannot guarantee high-quality meshes for arbitrarygeometries or for non-water-tight computer-aided design models. For reliablesimulations on such meshes, we consider FE meshes with tetrahedral andprismatic elements that have badly-shaped elements$-$tetrahedra with dihedralangles close to $0^\circ$ and $180^\circ$, and slender prisms with triangularfaces that have short edges$-$and agglomerate such `bad' elements withneighboring elements to form a larger polyhedral virtual element. On eachelement, the element-eigenvalue inequality is used to estimate the criticaltime step. For a suite of illustrative finite element meshes with $\epsilon$being a mesh-coordinate parameter that leads to poor mesh quality, we show thatadopting VEM on the agglomerated polyhedra yield critical time steps that areinsensitive as $\epsilon \rightarrow 0$. The significant reduction in solutiontime on meshes with agglomerated virtual elements vis-$\`a$-vis tetrahedralmeshes is demonstrated through explicit dynamics simulations on a tapered beam.

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