A homogenization theory for time-dependent nonlinear composites with periodic internal structures
type: Item
instance of: scholarly article
title: A homogenization theory for time-dependent nonlinear composites with periodic internal structures
zbMATH Open document ID: 0973.74007
DOI: 10.1016/S0020-7683(98)00236-4
author: V. Pereyra
published in: International Journal of Solids and Structures
publication date: 2001-11-16T00:00:00Z
review text: This paper describes a homogenization theory for time-dependent deformations (such as creep and viscoplasticity) of nonlinear composites with periodic internal structure, within the framework of infinitesimal strain. The theory is firstly developed in the macroscopically uniform case in a rate form, without resort to any asymptotic expansion, and then it is extended to the macroscopically nonuniform case in an incremental form, using an asymptotic expansion. Thus a macroscopic constitutive equation and a microscopic stress evolution equation are derived in rate and incremental forms by introducing two kinds of Y-periodic functions, which are determined by solving two unit cell problems. The resulting equations are shown to be effective for computing incrementally the time-dependent deformations for which the history of either macroscopic stress or macroscopic strain is prescribed. An application is considered to the transverse creep of metal matrix composites reinforced undirectionally with continuous fibers.
Mathematics Subject Classification ID: 74A40
Mathematics Subject Classification ID: 74Q15
Mathematics Subject Classification ID: 74E30
zbMATH DE Number: 1341385
zbMATH Keywords: homogenization theory
zbMATH Keywords: nonlinear composites
zbMATH Keywords: periodic internal structure
zbMATH Keywords: infinitesimal strain
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: macroscopic constitutive equation
zbMATH Keywords: microscopic stress evolution equation
zbMATH Keywords: transverse creep
zbMATH Keywords: metal matrix composites
zbMATH Keywords: fiber-reinforced composites
reviewed by: Marco Codegone
MaRDI profile type: Publication
full work available at URL: s0020-7683(98)00236-4
OpenAlex ID: W2035494196
description: scientific article; zbMATH DE number 1341385