Laminar Elastic Composites with Crystallographic Symmetry
- 1 June 1990
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 50 (3), 683-702
- https://doi.org/10.1137/0150040
Abstract
Francfort and Murat [Arch. Rational Mech. Anal., 94 (1986), pp. 307–334] derived an explicit formula for the effective elasticity tensor of a multiply layered composite made from two isotropic elastic materials in prescribed proportion. For multiply layered composites with crystallographic symmetry, it is shown that these formulae can be represented as a group average over the crystallographic group. The special case of cubically symmetric elastic composites made by multiple layering is considered. This article determines precisely the set of elasticity tensors that correspond to these composites. Extremal property of laminar composites is then used (see Avellaneda [SIAMJ. Appl. Math., 47 (1987), pp. 1216–1228]) to obtain new optimal bounds on the effective shear moduli for elastic composites with cubic symmetry.Keywords
This publication has 14 references indexed in Scilit:
- Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materialsArchive for Rational Mechanics and Analysis, 1988
- Variational bounds on the effective moduli of anisotropic compositesJournal of the Mechanics and Physics of Solids, 1988
- On the effective elasticity of a two-dimensional homogenised incompressible elastic compositeProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988
- Optimal Bounds and Microgeometries for Elastic Two-Phase CompositesSIAM Journal on Applied Mathematics, 1987
- Fine phase mixtures as minimizers of energyArchive for Rational Mechanics and Analysis, 1987
- Improved rigorous bounds on the effective elastic moduli of a composite materialJournal of the Mechanics and Physics of Solids, 1984
- On the existence of solutions to some problems of optimal design for bars and platesJournal of Optimization Theory and Applications, 1984
- Regularization of optimal design problems for bars and plates, part 2Journal of Optimization Theory and Applications, 1982
- New bounds on effective elastic moduli of two-component materialsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1982
- A variational approach to the theory of the elastic behaviour of multiphase materialsJournal of the Mechanics and Physics of Solids, 1963