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

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

Gil, Antonio J., Lee, Chun Hean, Bonet, Javier ORCID: 0000-0002-0430-5181 and Aguirre, Miquel (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. ISSN 0045-7825 (Print), 1879-2138 (Online) (doi:https://doi.org/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: Article
Additional Information: cited By 4
Uncontrolled Keywords: Fast dynamics; Fractional step; Geometric conservation law; Incompressible; Locking; Petrov-Galerkin
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Faculty / Department / Research Group: Vice-Chancellor's Group
Last Modified: 23 Mar 2017 09:58
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/14089

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