Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials
type: Item
instance of: scholarly article
title: Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials
zbMATH Open document ID: 0976.74010
DOI: 10.1016/S0022-5096(98)00106-9
author: Renaud Masson
author: A. Zaoui
published in: Journal of the Mechanics and Physics of Solids
publication date: 2001-12-30T00:00:00Z
review text: The paper deals with a new Hill-type formulation for rate-dependent elasto-plasticity. Recalling Kröner's vs. Hill's versions of nonlinear self-consistent model, the authors conclude that for the rate-dependent elasto-plasticity Kröner's approach is inadequate and that Hill's concept would be more appropriate in the rate-dependent case. Essential features of Hill's approach to the self-consistent modelling of nonlinear heterogeneous materials are the reduction of nonlinear homogenization procedure to a quasi-linear one through an adequate linearization process, and the derivation of self-consistent concentration equations for the solution of Eshelby-type problems. An alternative linearization method at the local level is adopted as a consistent affine formulation, in the specific context of rate-dependent elasto-plasticity. At each point of the representative volume element of a multiphase material and at any time instant, the authors derive the inelastic strain rate from a potential depending on internal parameters which are described by evolution equations. According to the proposed affine approach, for sufficiently large time, the authors derive the linearized constitutive equations for the total strain rate and for the rate of internal parameters. Using the solution of these differential equations for internal variables, simpler linearized constitutive equations are derived within the framework of rate-dependent elasto-plasticity. At any time a linear viscoplastic homogenization problem, in the presence of eigenstrains, has to be solved. By use of the correspondence principle, i.e. the Laplace-Carson transform, the problem is reduced to an elastic one. The authors put into evidence the following difficulties: a) due to the affine approach, the whole nonlinear problem has an implicit nature; b) due to the viscoelastic coupling, local and global responses need to be known not only at a fixed time, but also at any previous time. The authors undertake the following …
Mathematics Subject Classification ID: 74C10
Mathematics Subject Classification ID: 74E15
zbMATH DE Number: 1420278
zbMATH Keywords: rate-dependent elastoplasticity
zbMATH Keywords: nonlinear self-consistent model
zbMATH Keywords: nonlinear heterogeneous materials
zbMATH Keywords: linearization
zbMATH Keywords: concentration equations
zbMATH Keywords: homogenization
zbMATH Keywords: concentration tensors
zbMATH Keywords: affine formulation
zbMATH Keywords: internal parameters
zbMATH Keywords: evolution equations
zbMATH Keywords: correspondence principle
zbMATH Keywords: Laplace-Carson transform
zbMATH Keywords: iterative scheme
zbMATH Keywords: face-centred cubic polycrystals
reviewed by: Sanda Cleja-Ţigoiu
MaRDI profile type: Publication
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full work available at URL: s0022-5096(98)00106-9
OpenAlex ID: W2034639915
Wikidata QID: Q127097762
description: scientific article; zbMATH DE number 1420278