A variational formulation for nonlocal damage models
type: Item
instance of: scholarly article
title: A variational formulation for nonlocal damage models
zbMATH Open document ID: 1024.74005
DOI: 10.1016/S0749-6419(98)00057-6
published in: International Journal of Plasticity
publication date: 2003-11-16T00:00:00Z
review text: To control localization phenomena exhibited by strain softening constitutive relations, several issues have been proposed by various authors, based on spatial regularization. In this paper, the authors define a variational framework thought to encompass some of these issues: the constitutive relations are written at the structural scale, and take the form of minimization problems. The attention is restricted to standard generalized materials that depend on internal variables and their gradients. The general framework is defined, appearing as a variational formulation of the constitutive relations, and several related properties are pointed out, especially thermodynamical admissibility and some links with the work \textit{K.~C.~Valanis} [Acta Mech. 116, 1-14 (1996; Zbl 0858.73007)]. A numerical formulation of this variational principle is presented: it is expressed as a minimization problem, giving access to the various tools of mathematical optimization to solve the problem. The proposed framework is applied to several classes of models existing in the literature: a homogenization-based constitutive relation, a porosity model, and gradient plasticity. These models are shown to belong to the general framework, thus gaining a higher degree of generality and a quite simple numerical implementation, while a straightforward application of the variational principle gives rise to some remarkable properties.
reviewed by: Anatoliy S. Semenov
Mathematics Subject Classification ID: 74A45
Mathematics Subject Classification ID: 74R20
Mathematics Subject Classification ID: 74G65
zbMATH DE Number: 1440999
zbMATH Keywords: variational formulation
zbMATH Keywords: constitutive relations
zbMATH Keywords: energy methods
zbMATH Keywords: nonlocal damage
zbMATH Keywords: thermodynamical admissibility
zbMATH Keywords: homogenization
zbMATH Keywords: free energy
zbMATH Keywords: numerical variational framework
zbMATH Keywords: gradient plasicity
zbMATH Keywords: porosity
zbMATH Keywords: dissipation potentials
author: Eric Lorentz
author: S. Andrieux
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1440999