Implementation of a Model of Coupled Elastic-Plastic Unilateral Damage Material to Finite Element Code

Abstract

ABSTRACT:The continuum damage mechanics-based elasto-plastic damage theory, that extends the total form of Hayakawa and Murakami equations, is developed. Weak elastic-plastic dissipation coupling is assumed by the use of two dissipation potentials, plastic and damage, where only isotropic plasticity and damage hardening is included, whereas kinematic hardening is not accounted for. Unilateral damage condition, based on the concept of generalized projection operators, accounts for a partial damage deactivation, which allows for an influence of negative principal components of the stress tensor on damage evolution. The incremental representation of the elastic-damage constitutive equations is derived. Both elastic-damage and plastic-damage compliance matrices are developed for plane stress condition, and implemented to ABAQUS finite element code by the user-supplied procedure for non-standard material properties. Effective computation algorithm for plastic and damage loading/unloading conditions based on the doubly passive predictor and plastic-damage corrector approach is proposed. Numerical examples are presented by applying the model calibration by Hayakawa and Murakami for the spheroidized graphite cast iron FCD400. The examples illustrate the capability of the model to describe elastic-plastic damage evolution under monotonic loading. Under reverse loading conditions a partial elastic stiffness recovery was demonstrated on the consecutive increasing strain-controlled loading cycles and some limitation of the model was shown.KEY WORDS: elasto-plastic damage, damage-induced anisotropy, damage deactivation, stiffness recovery, doubly passive predictor-corrector approach.

Pseudo-potential of elastoplastic damage constitutive model and its application

“…The usual expressions of it are of two typical kinds of equations such as Helmholtz's and Gibbs'. According to their hypothesis, the dissipation energy makes up of the plastic and the damage parts (Chow and Lu, 1989;Zhu and Cescotto, 1995;Hayakawa et al, 1998;Kratzig and Polling, 2004;Miehe et al, 2002;Bielski et al, 2006). And also many writers considered the irreversible behavior as a plastic hardening mechanism (Ju, 1989;Murakami and Kamiya, 1997;Lubarda and Krajcinovic, 1995a,b;Krajcinovic, 1996;Wu and Nanakorn, 1999;Ragueneau et al, 2000;Cimetiere et al, 2005;Shao, 2007).…”

Numerical Analysis of FG and TBC Systems Based on Thermo-Elasto-Plastic-Damage Model

“…Bielski et al [18] extended this model to the incremental formulation d = C d , where C D stands for the effective tangent compliance tensor.…”

“…Since the plasticity and damage constitutive Eqs. (18)(19)(20)(21) are given in the incremental form, in order to solve coupled elasto-plastic-damage process we also need incremental form for equations (7).…”

Anisotropic damage–plasticity model for concrete

“…where the superscript ± designates tension, +, or compression, À, K ± is the tensile or compressive damage isotropic hardening functions, K AE ¼ K AE 0 when there is no damage, K AE 0 is the tensile or compressive initial damage parameter, L ijkl is a fourth-order symmetric tensor (Bielski et al, 2006;Lee et al, 1985;Hansen and Schreyer, 1994), and Y ij is the damage driving force that characterizes damage evolution and is interpreted here as the energy release rate (e.g. Voyiadjis and Kattan, 1992a,b, 1999Voyiadjis and Park, 1997b).…”