Why continuum damage is nonlocal: Justification by quasiperiodic microcrack array
type: Item
instance of: scholarly article
title: Why continuum damage is nonlocal: Justification by quasiperiodic microcrack array
zbMATH Open document ID: 0666.73067
DOI: 10.1016/0093-6413(87)90063-2
published in: Mechanics Research Communications
publication date: 1987-01-01T00:00:00Z
review text: Strain-softening damage due to distributed cracking is modeled by an elastic continuum with a quasiperiodic array of cracks of regular spacing but varying sizes. As a model for the initial stage, the cracks are penny-shaped and small compared to their spacing, and as a model for the terminal stage the uncracked ligaments between the cracks are circular and small compared to their spacing. The strain due to cracks and the compliance per crack are calculated. The cracked material is homogenized in such a manner that the macroscopic continuum strains satisfy exactly the condition of compatibility with the actual strains due to cracks, and the macroscopic continuum stress satisfies exactly the condition of work equivalence with the actual stresses in the cracked material. The results show that, contrary to the existing theories, the damage variable used in continuum damage mechanics should be nonlocal, while the elastic part of the response should be local. In particular, the nonlocal continuum damage should be considered as a function of the spatial average of the cracking strain rather than its local value. The size of the averaging region is determined by the crack spacing.
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4090960
zbMATH Keywords: Strain-softening damage
zbMATH Keywords: distributed cracking
zbMATH Keywords: elastic continuum with a quasiperiodic array of cracks
zbMATH Keywords: regular spacing
zbMATH Keywords: varying sizes
zbMATH Keywords: initial stage
zbMATH Keywords: penny-shaped and small
zbMATH Keywords: terminal stage
zbMATH Keywords: uncracked ligaments
zbMATH Keywords: circular and small
zbMATH Keywords: strain
zbMATH Keywords: compliance per crack
zbMATH Keywords: homogenized
zbMATH Keywords: condition of compatibility
zbMATH Keywords: condition of work equivalence
zbMATH Keywords: function of the spatial average
author: Zdeněk P. Bažant
MaRDI profile type: Publication
full work available at URL: 0093-6413(87)90063-2
OpenAlex ID: W2153566274
description: scientific article; zbMATH DE number 4090960