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Pré-Publication, Document De Travail Année : 2017

A Hybrid High-Order method for nonlinear elasticity *

Michele Botti
Daniele Di Pietro
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Résumé

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in two and three space dimensions, it supports general meshes including polyhedral elements and nonmatching interfaces, enables arbitrary approximation order, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Additionally, the method satisfies a local principle of virtual work on each mesh element, with interface tractions that obey the law of action and reaction. A complete analysis covering very general stress-strain laws is carried out, and optimal error estimates are proved. Extensive numerical validation on model test problems is also provided on two types of nonlinear models.
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Dates et versions

hal-01539510 , version 1 (15-06-2017)
hal-01539510 , version 2 (07-07-2017)

Identifiants

  • HAL Id : hal-01539510 , version 1

Citer

Michele Botti, Daniele Di Pietro, Pierre Sochala. A Hybrid High-Order method for nonlinear elasticity *. 2017. ⟨hal-01539510v1⟩
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