Linear Elasticity of Planar Delaunay Networks: Random Field Characterization of Effective Moduli

A study is conducted of the influence of microscale geometric and physical randomness on effective moduli of a continuum approximation of disordered microstruetures. A particular class of microstructures investigated is that of planar Delaunay networks made up of linear elastic rods connected by joints. Three types of networks are considered: Delaunay networks with random geometry and random spring constants, modified Delaunay networks with random geometry and random spring constants, and regular triangular networks with random spring constants. Using a structural mechanics method, a numerical study is conducted of the first and second order characteristics of random fields of effective moduli. In view of duality of the Delaunay triangulations to the Voronoi tessellations, these results provide the basis for development of analytical models of various heterogeneous solids, e.g. granular, fibrous.