DETERMINATION OF ELASTIC PROPERTIES OF VERY HETEROGENEOUS MEDIA WITH CELLULAR-AUTOMATA

A cellular automaton is used to calculate the elastic properties of ve ry heterogeneous media. The lattice gas method (designed to model visc ous flow) is applied to elastic problems through the correspondence be tween the steady state velocity field in an incompressible Newtonian f luid at low Reynolds number and the displacement field in an incompres sible elastic solid. The cellular automaton is applied to determine th e elastic properties of a matrix containing randomly distributed hard inclusions. Because the equations of equilibrium are locally solved fo r any distribution of the inclusion phase, the method provides a means to estimate the influence of stress field perturbations on the macros copic properties of heterogeneous systems. The effective elastic shear modulus is calculated as a function of the concentration C of the inc lusion phase (0 less than or equal to C less than or equal to 1) for d ifferent values of R, the rheological contrast between the inclusion a nd the matrix. The numerical results are compared with those obtained by various micromechanical models. Estimates given by the cellular aut omaton agree with the analytical solution for a double periodic triang ular system of discs. However, the effective shear modulus for the cel lular automaton fluid does not fall within the limits of Hashin and Sh trikman. It follows the same trend as that of the lower bound but stay s below the lower bound for all concentrations. Likewise, the shear mo dulus for a cellular automaton fluid is also systematically lower than that predicted by the differential method, although the trends are si milar.