A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics

Gil, A. J., Lee, C. H. , Bonet, J. and Aguirre, M. (2014) A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics. Computer Methods in Applied Mechanics and Engineering, 276, pp. 659-690. (doi: 10.1016/j.cma.2014.04.006)

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Abstract

A mixed second order stabilised Petrov–Galerkin finite element framework was recently introduced by the authors (Lee et al., 2014) [46]. The new mixed formulation, written as a system of conservation laws for the linear momentum and the deformation gradient, performs extremely well in bending dominated scenarios (even when linear tetrahedral elements are used) yielding equal order of convergence for displacements and stresses. In this paper, this formulation is further enhanced for nearly and truly incompressible deformations with three key novelties. First, a new conservation law for the Jacobian of the deformation is added into the system providing extra flexibility to the scheme. Second, a variationally consistent Petrov–Galerkin stabilisation methodology is derived. Third, an adapted fractional step method is presented for both incompressible and nearly incompressible materials in the context of nonlinear elastodynamics. For completeness and ease of understanding, these three improvements are presented both in small and large strain regimes, studying the eigenstructure of the resulting systems. A series of numerical examples are presented in order to demonstrate the robustness of the enhanced methodology with respect to the work previously published by the authors.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Lee, Dr Chun Hean
Authors: Gil, A. J., Lee, C. H., Bonet, J., and Aguirre, M.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
Journal Abbr.:CMAME
Publisher:Elsevier
ISSN:0045-7825
ISSN (Online):1879-2138
Published Online:26 April 2014

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