STOCHASTIC PARALLEL-BRITTLE NETWORKS FOR MODELING MATERIALS

The behavior of Voronoi-Delaunay parallel-brittle networks of truss el ements as models for material behavior is studied. Means and variances of both the number of elements in a network and their length are give n. The uniaxial stiffness of the networks is found equal to the elemen t axial stiffness. The expected value of the network's uniaxial-tensil e strength is proportional to the square root of the expected number o f elements and to the expected value of the strength of the elements. The toughness of the networks is proportional to the square of the exp ected value of element strength and to the square root of the expected number of elements. An application to pullout of an anchor is present ed. Daniels systems and chain-of-bundles systems are also analyzed to provide perspective. Statistical size effects for parallel-brittle net works are quite different form those associated with weak-link systems .