Damage patterns and constitutive response of random matrix-inclusion composites

Out-of-plane responses of disordered matrix-inclusion composites are studied as spatially cooperative phenomena of initiation and propagation of cracks; both phases (of matrix and inclusions) are locally isotropic and elastic-brittle. The tool is a numerical simulation method based on a very fine two-dimensional spring network, whereby damage evolution is simulated by sequentially removing/ breaking bonds in this lattice in accordance with the local state of stress/strain concentrations. Two parameters - stiffness ratio and strain-to-failure ratio of both phases - define a damage plane onto which various aspects of the system's response are being mapped, thereby resulting in damage maps. The main focus of the study is on a basic classification and statistical scatter of effective constitutive responses, as well as on the accompanying geometric patterns of damage. Additionally, an investigation of the damage sensitivity of periodic composites to very weak perturbations in geometry and material properties is carried out. The paper concludes with a proposal for a model of stress-strain responses by a jump Markov process.