On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media

Y. Benveniste, G. J. Dvorak, T. Chen

Research output: Contribution to journalArticle

147 Citations (Scopus)

Abstract

The existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models. The dilute approximation gives symmetric estimates for all matrix-based multiphase media. The Mori-Tanaka and the self-consistent methods do so for all two-phase systems, but only for those multiphase systems where the dispersed inclusions have a similar shape and alignment. However, the differential schemes associated with the self-consistent method can predict diagonally symmetric overall stiffness and compliance for multiphase systems of arbitrary phase geometry. A related question is raised about the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors. A direct estimate follows from each of the above models, whereas Levin's results [Mechanics of Solids 2, 58 (1967)] permit an indirect evaluation in terms of the estimated overall mechanical properties or concentration factors and phase thermoelastic moduli. These two results are shown to coincide for those systems and models which return diagonally symmetric estimates of the overall stiffness. Finally, model predictions of the overall elastic symmetry of composite media are discussed with regard to the spatial distribution of the phases.

Original languageEnglish
Pages (from-to)927-946
Number of pages20
JournalJournal of the Mechanics and Physics of Solids
Volume39
Issue number7
DOIs
Publication statusPublished - 1991

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Tensors
stiffness
Stiffness
tensors
symmetry
estimates
binary systems (materials)
evaluation
stress tensors
thermal stresses
Thermal stress
Spatial distribution
equivalence
Mechanics
spatial distribution
alignment
mechanical properties
inclusions
Mechanical properties
composite materials

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media. / Benveniste, Y.; Dvorak, G. J.; Chen, T.

In: Journal of the Mechanics and Physics of Solids, Vol. 39, No. 7, 1991, p. 927-946.

Research output: Contribution to journalArticle

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AU - Chen, T.

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AB - The existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models. The dilute approximation gives symmetric estimates for all matrix-based multiphase media. The Mori-Tanaka and the self-consistent methods do so for all two-phase systems, but only for those multiphase systems where the dispersed inclusions have a similar shape and alignment. However, the differential schemes associated with the self-consistent method can predict diagonally symmetric overall stiffness and compliance for multiphase systems of arbitrary phase geometry. A related question is raised about the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors. A direct estimate follows from each of the above models, whereas Levin's results [Mechanics of Solids 2, 58 (1967)] permit an indirect evaluation in terms of the estimated overall mechanical properties or concentration factors and phase thermoelastic moduli. These two results are shown to coincide for those systems and models which return diagonally symmetric estimates of the overall stiffness. Finally, model predictions of the overall elastic symmetry of composite media are discussed with regard to the spatial distribution of the phases.

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