Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Extension to nearly incompressible implicit and explicit elastodynamics in finite strains

Kadapa, Chennakesava

Abstract

We present a novel unified finite element framework for performing computationally efficient large strain implicit and explicit elastodynamic simulations using triangular and tetrahedral meshes that can be generated using the existing mesh generators. For the development of a unified framework, we use Bézier triangular and tetrahedral elements that are directly amenable for explicit schemes using lumped mass matrices and employ a mixed displacement-pressure formulation for dealing with the numerical issues arising due to volumetric and shear locking. We demonstrate the accuracy of the proposed scheme by studying several challenging benchmark problems in finite strain elastostatics and nonlinear elastodynamics modelled with nearly incompressible hyperelastic and von Mises elastoplastic material models. We show that Bézier elements, in combination with the mixed formulation, help in developing a simple unified finite element formulation that is accurate, robust, and computationally very efficient for performing a wide variety of challenging nonlinear elastostatic and implicit and explicit elastodynamic simulations.

Citation

Kadapa, C. (2019). Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Extension to nearly incompressible implicit and explicit elastodynamics in finite strains. International Journal for Numerical Methods in Engineering, 119(2), 75-104. https://doi.org/10.1002/nme.6042

• Journal Article Type: Article
• Acceptance Date: Feb 12, 2019
• Online Publication Date: Mar 4, 2019
• Publication Date: Jul 13, 2019
• Deposit Date: Aug 29, 2022
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Electronic ISSN: 1097-0207
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 119
• Issue: 2
• Pages: 75-104
• DOI: https://doi.org/10.1002/nme.6042
• Keywords: Bézier elements, explicit elastodynamics, mixed formulation, nonlinear dynamics, Taylor impact bar
• Public URL: http://researchrepository.napier.ac.uk/Output/2893865