Stochastic Parallel-Brittle Networks for Modeling Materials

Abstract

The behavior of Voronoi-Delaunay parallel-brittle networks of truss elements as models for material behavior is studied. Means and variances of both the number of elements in a network and their length are given. The uniaxial stiffness of the networks is found equal to the element axial stiffness. The expected value of the networks' uniaxial-tensile strength is proportional to the square root of the expected number of elements and to the expected value of the strength of the elements. The toughness of the networks is proportional to the square of the expected value of element strength and to the square root of the expected number of elements. An application to pullout of an anchor is presented. Daniels systems and chain-of-bundles systems are also analyzed to provide perspective. Statistical size effects for parallel-brittle networks are quite different from those associated with weak-link systems.