Strain- and stress-based continuum damage models. I. Formulation
type: Item
instance of: scholarly article
title: Strain- and stress-based continuum damage models. I. Formulation
zbMATH Open document ID: 0634.73106
DOI: 10.1016/0020-7683(87)90083-7
author: B. George
published in: International Journal of Solids and Structures
publication date: 1987-01-01T00:00:00Z
review text: Continuum elastoplastic damage models employing irreversible thermodynamics and internal state variables are developed within two alternative dual frameworks. In a strain [stress]-based formulation, damage is characterized through the effective stress [strain] concept together with the hypothesis of strain [stress] equivalence, and plastic flow is introduced by means of an additive split of the stress [strain] tensor. In a strain-based formulation we redefine the equivalent strain, usually defined as the \(J_ 2\)-norm of the strain tensor, as the (undamaged) energy norm of the strain tensor. In a stress-based approach we employ the complementary energy norm of the stress tensor. These thermodynamically motivated definitions result, for ductile damage, in symmetric elastic-damage moduli. For brittle damage, a simple strain- based anisotropic characterization of damage is proposed that can predict crack development parallel to the axis of loading (splitting mode). The strain- and stress-based frameworks lead to dual but not equivalent formulations, neither physically nor computationally. A viscous regularization of strain-based, rate-independent damage models is also developed, with a structure analogous to viscoplasticity of the Perzyna type, which produces retardation of microcrack growth at higher strain rates. This regularization leads to well-posed initial value problems. Application is made to the cap model with an isotropic strainbased damage mechanism. Comparisons with experimental results and numerical simulations are undertaken in Part II of this work.
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 4033293
zbMATH Keywords: Continuum elastoplastic damage models
zbMATH Keywords: internal state variables
zbMATH Keywords: dual frameworks
zbMATH Keywords: strain-based formulation
zbMATH Keywords: stress-based approach
zbMATH Keywords: complementary energy norm
zbMATH Keywords: ductile damage
zbMATH Keywords: symmetric elastic-damage moduli
zbMATH Keywords: brittle damage
zbMATH Keywords: simple strain-based anisotropic characterization
zbMATH Keywords: splitting mode
zbMATH Keywords: viscous regularization
zbMATH Keywords: rate-independent damage models
zbMATH Keywords: viscoplasticity of the Perzyna type
MaRDI profile type: Publication
full work available at URL: 0020-7683(87)90083-7
OpenAlex ID: W2052815421
description: scientific article; zbMATH DE number 4033293