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 ≥ 1 on the mesh skeleton, together with cell-based poly-nomials 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.
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Mickaël Abbas, Alexandre Ern, Nicolas Pignet. A Hybrid High-Order method for incremental associative plasticity with small deformations. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2019, 346, pp.891-912. ⟨https://www.sciencedirect.com/science/article/pii/S0045782518304353⟩. ⟨10.1016/j.cma.2018.08.037⟩. ⟨hal-01768411v4⟩

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