A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework

TL;DR

This paper introduces a novel Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework, emphasizing accuracy, mesh flexibility, and computational efficiency.

Contribution

The paper presents a new HHO method that supports polyhedral meshes, avoids volumetric locking, and simplifies integration, advancing numerical simulation of finite plasticity.

Findings

Supports polyhedral meshes with non-matching interfaces

Free of volumetric locking in simulations

Achieves symmetric tangent matrices in Newton's method

Abstract

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.