Abstract
A variational structure developed over the last few years by the author is applied to the estimation of the overall behavior of a composite material, in the regime of small strains but physically nonlinear response. The composite is modeled as nonlinearly elastic and the results take the form of stationary estimates for the overall energy and complementary energy functions. Simple explicit formulas are derived for the cases of a nonlinear matrix reinforced by rigid inclusions or weakened by voids, distributed with any two-point statistics. Detailed implications are developed for an incompres-sible isotropic matrix containing an isotropic distribution of voids. The uniaxial stress-strain behavior of the matrix is arbitrary (apart from mild restrictions). Numerical results are presented for “linear plus power-law” matrix behavior.
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© 1990 Springer-Verlag New York Inc.
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Willis, J.R. (1990). Variational Estimates for the Overall Behavior of a Nonlinear Matrix—Inclusion Composite. In: Weng, G.J., Taya, M., Abé, H. (eds) Micromechanics and Inhomogeneity. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8919-4_36
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DOI: https://doi.org/10.1007/978-1-4613-8919-4_36
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