The mechanical properties of materials with interconnected cracks and pores

This paper studies the effect on the overall properties of a cracked solid of the existence of connections between otherwise isolated cracks and of small-scale porosity within the ‘solid’ material. The intention is to provide effective medium models for the calculation of elastic wave propagation with wavelengths greater than the dimensions of the cracks. The method follows that of earlier papers in which the overall elastic properties are directly related to parameters governing the microstructure, such as crack number density and the mean radius and spacing distance of the cracks. Expressions derived by the method of smoothing are evaluated to second order in the number density of cracks, thereby incorporating crack–crack interactions through both the strain field in the solid and the flow field of fluids in the pores. Flow of interstitial liquids tends to weaken the material; the limit of zero flow is equivalent to isolating the cracks and the limit of free flow is equivalent to dry (gas-filled) cracks. It also introduces additional attenuation. The inclusion of small-scale porosity gives a model of ‘equant porosity’ which is more closely constrained by the details of crack dynamics than earlier models.