Homogenization of fissured elastic solids in the presence of unilateral conditions and friction
type: Item
instance of: scholarly article
title: Homogenization of fissured elastic solids in the presence of unilateral conditions and friction
zbMATH Open document ID: 0723.73010
DOI: 10.1007/BF00350517
published in: Computational Mechanics
publication date: 1990-01-01T00:00:00Z
review text: The aim of the paper is to obtain the overall behaviour of some cracked bodies. The effective solids should be without fissures and approximate the behaviour of the real fissured bodies. A homogenization method may by used for elastic solids with periodically distributed microfissures. Detailed bibliography on the subject is given by the author. The present contribution extends the previous results of the literature by considering a three-dimensional problem with nonrectilinear fissures and taking friction into account. It deals with a three-dimensional linear hyperelastic solid weakened by periodically distributed microfissures in the presence of the Signorini's conditions with friction. The size of the fissures is not supposed to be small in comparison with dimensions of the period. The friction conditions may be anisotropic and nonconvex. The friction laws are assumed in the subdifferential form. Two homogenization problems are investigated. The first problem is purely static with a friction law of deformational plasticity type. An implicit variational inequality posed on the periodic cracked domain has to be homogenized. The local problem has the same form but posed on the period. The displacement approach and the alternative stress approach are studied. The second homogenization problem is a quasi-static one. The subdifferential friction law is of the flow law type. This leads to additional difficulties, because the variational formulation is available in the form of an implicit variational inequality coupled with a variational inequality. In both cases, the macroscopic behaviour is elasto-plastic of nonstandard type with hardening and possibly softening.
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 4193205
zbMATH Keywords: periodically distributed microfissures
zbMATH Keywords: three-dimensional problem
zbMATH Keywords: nonrectilinear fissures
zbMATH Keywords: linear hyperelastic solid
zbMATH Keywords: Signorini's conditions
zbMATH Keywords: purely static
zbMATH Keywords: friction law of deformational plasticity type
zbMATH Keywords: implicit variational inequality
zbMATH Keywords: displacement approach
zbMATH Keywords: alternative stress approach
zbMATH Keywords: quasi-static
zbMATH Keywords: subdifferential friction law
zbMATH Keywords: flow law type
zbMATH Keywords: implicit variational inequality coupled with a variational inequality
author: J. J. Telega
reviewed by: Thérèse Lévy
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00350517
OpenAlex ID: W2044362051
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description: scientific article; zbMATH DE number 4193205