The second-order procedure: Exact vs approximate results for isotropic, two-phase composites
type: Item
instance of: scholarly article
title: The second-order procedure: Exact vs approximate results for isotropic, two-phase composites
zbMATH Open document ID: 0990.74052
DOI: 10.1016/S0022-5096(99)00005-8
published in: Journal of the Mechanics and Physics of Solids
publication date: 2002-08-19T00:00:00Z
review text: The authors investigate the effect of relaxing the proportional strain hypothesis used by the second author [ibid. 44, No. 6, 827-862 (1966; Zbl 1054.74708)] in the context of second-order estimates for effective behaviour of three-dimensional statistically isotropic two-phase nonlinearly or viscous composites. It is found that this hypothesis does not hold in general, but it leads to fairly small errors. Finally, it is emphasized that the improvement given in this paper affects only three-dimensional statistically isotropic two-phase systems.
Mathematics Subject Classification ID: 74Q20
Mathematics Subject Classification ID: 74E30
zbMATH DE Number: 1428447
zbMATH Keywords: average strain deviator
zbMATH Keywords: Hashin-Shtrikman estimate
zbMATH Keywords: reinforced material
zbMATH Keywords: isotropic two-phase composites
zbMATH Keywords: proportional strain hypothesis
zbMATH Keywords: second-order estimates
author: Michael V. Nebozhyn
author: Pedro Ponte Castañeda
reviewed by: Dan Polisevski
MaRDI profile type: Publication
cites work: Second–order estimates of the self–consistent type for viscoplastic polycrystals
cites work: A variational approach to the theory of the elastic behaviour of multiphase materials
cites work: Q5833606
cites work: Continuum micro-mechanics of elastoplastic polycrystals
cites work: Variational estimates of the self-consistent type for the effective behaviour of some model nonlinear polycrystals
cites work: Exact second-order estimates for the effective mechanical properties of nonlinear composite materials.
cites work: Nonlinear electrical conductivity in heterogeneous media
cites work: Q4836602
cites work: Q4379920
cites work: Q4838117
cites work: Some simple explicit bounds for the overall behaviour of nonlinear composites
cites work: Bounds and self-consistent estimates for the overall properties of anisotropic composites
cites work: Variational and Related Methods for the Overall Properties of Composites
full work available at URL: s0022-5096(99)00005-8
OpenAlex ID: W1979531064
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description: scientific article; zbMATH DE number 1428447