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A second-order homogenization method in finite elasticity and applications to black-filled elastomers. (English) Zbl 0984.74070

Summary: We develop an analytical method for estimating the macroscopic behavior of heterogeneous elastic systems subjected to finite deformations. The objective is to generate variational estimates for the effective or homogenized stored-energy function of hyperelastic composites, which will be accomplished by means of a suitable generalization of the “second-order procedure” [the first author, ibid. 44, No. 6, 827-862 (1996)]. The key idea in this method is the introduction of an optimally chosen “linear thermoelastic comparison composite,” which can then be used to convert available homogenization estimates for linear systems directly into new estimates for nonlinear composites. To illustrate the method, an application is given for carbon-black filled elastomers, and estimates analogous to the well-known Hashin-Shtrikman estimates and self-consistent estimates for linear-elastic composites are generated.

MSC:

74Q20 Bounds on effective properties in solid mechanics
74E30 Composite and mixture properties
74B20 Nonlinear elasticity
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