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

Abstract

Summary 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 ≥ 1 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 nonmatching interfaces, and is free of volumetric locking. In addition, 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 comparisons against known solutions obtained with an industrial software using conforming and mixed finite elements.

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

“…In addition, HHO discretisations of hyperelastic materials in small and finite deformations were presented in [34] and [15], respectively. HHO discretisations for problems involving plastic and elastoplatic simulations are discussed in [16,17], whereas contact phenomena are addressed in [66].…”

A Hybrid High-Order Method for the Mixed Steklov Eigenvalue Problem

“…HHO methods have been used extensively mainly in the context of computational mechanics, for example solid mechanics [1,2,3], contact problems [16], obstacle problems [19] and fluid mechanics [15,11]. Recent applications include acoustic time-dependent wave problems [12,13], magnetostatics [17], and time-harmonic Maxwell equations [20].…”

Time-explicit hybrid high-order method for the nonlinear acoustic wave equation

“…The HHO method was introduced for linear diffusion in [25] and for linear elasticity in [24]. It was extended to various applications such as solid mechanics with the Biot problem [7], nonlinear elasticity [8], hyperelasticity [1] and elastoplasticity [2,3]. The HHO method belongs to the class of hybridizable discontinuous Galerkin (HDG) methods [19], as shown in [17].…”