A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework
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| Format: | Preprint |
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2019
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| _version_ | 1866913619301629952 |
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| author | Abbas, Mickaël Ern, Alexandre Pignet, Nicolas |
| author_facet | Abbas, Mickaël Ern, Alexandre Pignet, Nicolas |
| contents | We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The HHO method leads to a primal formulation, supports polyhedral meshes with non-matching interfaces, is free of volumetric locking, the integration of the behavior law is performed only at cell-based quadrature nodes, and the tangent matrix in Newton's method is symmetric. Moreover, the principle of virtual work is satisfied locally with equilibrated tractions. Various two- and three-dimensional benchmarks are presented, as well as comparison against known solutions with an industrial software using conforming and mixed finite elements. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1901_04480 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework Abbas, Mickaël Ern, Alexandre Pignet, Nicolas Computational Engineering, Finance, and Science Numerical Analysis We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The HHO method leads to a primal formulation, supports polyhedral meshes with non-matching interfaces, is free of volumetric locking, the integration of the behavior law is performed only at cell-based quadrature nodes, and the tangent matrix in Newton's method is symmetric. Moreover, the principle of virtual work is satisfied locally with equilibrated tractions. Various two- and three-dimensional benchmarks are presented, as well as comparison against known solutions with an industrial software using conforming and mixed finite elements. |
| title | A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework |
| topic | Computational Engineering, Finance, and Science Numerical Analysis |
| url | https://arxiv.org/abs/1901.04480 |