INTRODUCTION
The generation and propagation of microcracks in relation to the loading conditions, packing arrangement, grain sizes and shapes is essential for understanding the stress-strain relationships and quasi-brittle fracture of granular materials. Experiments have shown that local stresses in individual grains are important in the overall response of granular materials[ 1]. At a microscopic level, local stresses are related to: 1) tensile strength of grains; 2) geometry; 3) pores; 4) grain contacts. How can we quantify the micro-structure and the distribution of stresses? Once quantified, how are these parameters related to the macro mechanical behavior? Which parameter is dominant in defining the macro-mechanical properties such as stress-strain relationship and failure of materials? In this paper we will use a two-dimensional numerical model based on the elastic interaction and tensile fracture of grains and grain bonds to study the effects of heterogeneity in grain strengths on macroscopic strain-hardening and strain-softening deformation, and fracture under differential compressive stresses.
