Heterogeneity in engineering materials: Cases of discrete and statistical disorder.

Abstract

This paper presents analytical and numerical models for simulation of elastic and fracture properties of heterogeneous materials such as fiber composite and concrete. When the nonhomogeneous material is idealized as an elasticity problem it is possible to analyze and solve it by Papkovich-Neuber displacement potentials. The paper examines the elastic fields generated by two elliptic and three circular inclusions. The inhomogeneities undergo either eigenstrain expansion or mechanical loading on the matrix in which they are imbedded. Perfectly bonded and slipping interfaces are compared and expressed in infinite series. The results are illustrated by two specific geometries. When the heterogeneous material is composed of not only inclusions but also random voids, microcracks, material gradients, etc., the analytic classical elasticity approach is inconvenient. Hence, simulation is performed using a linear elastic-brittle framework. It is then possible to numerically study the elastic, and more importantly, the fracture characteristics of the solid. Possible fractal dimensions representing roughness are found for correlated Gaussian random materials under various loading conditions. Multifractal properties of the crack dissipation energy are illustrated by the f(α) spectrum. Finally, the correlation between the multifractal properties and the p model is demonstrated.