A Hybrid High-Order method for incremental associative plasticity with small deformations

Abstract

We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge 1$ on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The HHO method supports polyhedral meshes with non-matching interfaces, is free of volumetric-locking and the integration of the behavior law is performed only at cell-based quadrature nodes. Moreover, the principle of virtual work is satisfied locally with equilibrated tractions. Various two- and three-dimensional test cases from the literature are presented including comparison against known solutions and against results obtained with an industrial software using conforming and mixed finite elements.

arXiv comment28 pages, 26 figures, preprint

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Cited by in corpus (5)

• HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
• Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
• Hybrid coupling of CG and HDG discretizations based on Nitsche's method
• BR2 discontinuous Galerkin methods for finite hyperelastic deformations
• A quasi-optimal variant of the Hybrid High-Order method for elliptic PDEs with $H^{-1}$ loads