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Self-Consistent Methods for Composites : Vol.2: Wave Propagation in Heterogeneous Materials
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Self-Consistent Methods for Composites: Vol.1: Static Problems Solid Mechanics and Its Applications
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We use the equivalent inclusion method to write out expressions for the Helmholtz and Gibbs free energy of the inhomogeneity as quadratic forms in the intrinsic strains and strains at infinity. The solutions for some important particular cases are written out by asymptotically expanding the general solution in small parameters. The parameters determining the type of the asymptotic behavior are the inclusion semiaxis ratio and the inclusion-to-matrix elastic modulus ratio. We consider various physical situations arising when studying needle- and disk-shaped inclusions and characterized by various order of passage to the limit.
We analyze the applicability domains of the asymptotics by reduction to a single small parameter. For the case in which the parameters considerably differ from unity simultaneously, we single out seven domains corresponding to various relations between these parameters. We construct the diagrams of relative error isolines for the resulting tensors corresponding to the energy contribution from various strain tensor components.
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