Linear elasticity of planar Delaunay networks. III: Self-consistent approximations
[For parts I, II see the first author and \textit{C. Wang}, Acta Mech. 80, No. 1/2, 61-80 (1989; Zbl 0711.73275); ibid. 84, No. 1, 47-61 (1990; Zbl 0719.73047).] Two-phase Delaunay and regular triangular networks, with randomness per vertex, provide generic models of granular media consisting of two types of grains -- soft and stiff. We investigate effective macroscopic moduli of such networks for the whole range of area fractions of both phases and for a very wide range of stiffness of both phases. Results of computer simulations of such networks under periodic boundary conditions are used to determine which of several different self-consistent models can provide the best possible approximation to effective Hooke's law. The main objective is to find the effective moduli of a Delaunay network as if it was a field of inclusions, rather than vertices connected by elastic edges, without conducting the computer-intensive calculations of large windows.
two-dimensional matrix-inclusion composites
scientific article; zbMATH DE number 885789
scientific article