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

TL;DR

This paper introduces a Hybrid High-Order (HHO) numerical method for incremental associative plasticity in small deformation scenarios, supporting complex meshes and ensuring accuracy without volumetric-locking.

Contribution

The paper presents a novel HHO method that efficiently handles polyhedral meshes, local elimination of cell unknowns, and accurate integration for plasticity problems.

Findings

Supports polyhedral meshes with non-matching interfaces

Free of volumetric-locking effects

Accurate results comparable to industrial software

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 $k\ge1$ 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.