The nonlinear response of Boolean models: elasticity and conductivity

Abstract : The effective response of an ideal random composite, the Boolean model of spheres, with a nonlinear powerlaw matrix, is investigated. Nonlinearity is parametrized by the law exponent 0≤n≤1, with the values n=1 corresponding to a linear-elastic matrix and n=0 to a strongly nonlinear elastic matrix. To strengthen the effect of the microstructure, inclusions are either quasi-rigid or porous, whereas the matrix is compressible or incompressible. Full-fields solutions are computed numerically using Fourier methods, for varying inclusion volume fractions and nonlinearity exponent. Next, we consider the effect of a two-scale dispersion of pores and rigid inclusions in the context of a nonlinear matrix.
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Contributor : François Willot <>
Submitted on : Sunday, August 12, 2018 - 4:30:33 PM
Last modification on : Monday, November 12, 2018 - 11:02:52 AM


  • HAL Id : hal-01856565, version 1


François Willot, Dominique Jeulin. The nonlinear response of Boolean models: elasticity and conductivity. Physics & Mechanics of Random Media: from Morphology to Material Properties, pp.181, 2018, 978-2-35671-529-6. ⟨hal-01856565⟩



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