A MICROMECHANICAL DAMAGE THEORY FOR BRITTLE MATERIALS WITH SMALL CRACKS

Abstract

For brittle solids containing numerous small cracks, a micromechanical damage theory is presented which accounts for the interactions between different small cracks and the effect of the boundary of a finite solid, and includes growth of the pre‐existing small cracks. The analysis is based on a superposition scheme and series expansions of the complex potentials. The small crack evolution process is simulated through the use of fracture mechanics incorporating appropriate failure criteria. The stress–strain relations are obtained from the micromechanics analysis. Typical examples are given to illustrate the potential capability of the proposed theory. These results show that the present method provides a direct and efficient approach to deal with brittle finite solids containing multiple small cracks. The stress–strain relation curves are evaluated for a rectangular plate containing small cracks.