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.