Localizing Implicit Gradient Damage Based Treatment of Softening in Elasto-Plasticity

Abstract

As opposed to brittle fracture, the failure of ductile materials is preceded by severe plastic deformations. Microscopic mechanisms i.e., void growth and coalescence result in macroscopic property degradation causing softening, localization, and finally macroscopic crack. This contribution focuses on softening in elasto-plasticity and its mesh-objective description using an implicit gradient type of non-local damage mechanics framework. As reported in several studies Geers et al. (1998), Poh and Sun (2017), artificial widening of localization zone is observed when conventional implicit gradient type regularization is used. To circumvent this non-physical artifact, localizing implicit gradient damage (LIGD) formulation that is motivated by higher order continuum arguments, is adopted, Poh and Sun (2017). As opposed to previous remedies to artificial widening of the localization zone, LIGD proposes an internal length scale that decreases with deformation. A two-field (displacement-non-local equivalent plastic strain) hexahedra and a three-field (displacement-pressure-non-local equivalent plastic strain) tetrahedra element are formulated and implemented in commercial finite element software Abaqus through user element (UEL) subroutine. The effectiveness of the approach is demonstrated by solving two numerical examples. © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya