On a geometrically nonlinear damage model based on a multiplicative decomposition of the deformation gradient and the propagation of microcracks
type: Item
instance of: scholarly article
title: On a geometrically nonlinear damage model based on a multiplicative decomposition of the deformation gradient and the propagation of microcracks
zbMATH Open document ID: 1049.74007
DOI: 10.1016/S0022-5096(01)00092-8
author: R. Smith
published in: Journal of the Mechanics and Physics of Solids
publication date: 2002-06-27T00:00:00Z
review text: The aim is to derive a damage model for materials damaged by microcracks. The damage evolution equations are based on micromechanical considerations. The aim is to describe the brittle damage, when no macroscopic plastic deformation occurs. The micromechanics of crack propagation in a unit cell containing a crack is purely based on a variational principle for elastic body containing a crack in equilibrium, leading to the principle of maximum energy release rate. From this it follows the path of a growing crack by introducing a series of thermodynamically equivalent straight cracks. The equivalence of the energy dissipated by microcrack growth and the damage dissipation leads to a damage evolution law. This evolution law is embedded in a finite deformation framework based on a multiplicative decomposition into elastic and damage parts. As a consequence, an anisotropic damaged elasticity tensor is presented with the help of push and pull operations. The connection of the approach to other well-known damage theories is shown, and the advantages of a finite element framework are discussed. Numerical excamples show the possibilities of the proposed model.
Mathematics Subject Classification ID: 74A45
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74G65
zbMATH DE Number: 1761043
zbMATH Keywords: variational principle
zbMATH Keywords: finite deformation
zbMATH Keywords: anisotropic damage
reviewed by: Christina Papenfuß
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1761043