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arXiv · 1910.09459

A virtual element method for isotropic hyperelasticity

Daniel van Huyssteen·Batmanathan Dayanand Reddy
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Abstract

This work considers the application of the virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known strain energy functions, including neo-Hookean, Mooney-Rivlin and Ogden material models. For each of the strain energy functions the performance of the method under varying degrees of compressibility, including near-incompressibility, is investigated. Through these examples the convergence behaviour of the virtual element method is demonstrated. Furthermore, the method is found to be robust and locking free for a variety of element geometries, including elements with a high degree of concavity.

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Daniel van Huyssteen, Batmanathan Dayanand Reddy. 2019-10-21. A virtual element method for isotropic hyperelasticity. https://doi.org/10.1016/j.cma.2020.113134

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