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A hybrid high-order method for incremental associative plasticity with small deformations. (English) Zbl 1440.74368

Summary: 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 \(k\geq 1\) 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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)

Software:

MFront; HYPLAS
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Full Text: DOI arXiv

References:

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