Wave resistance in crack propagation: Lattices and homogeneous structured media

Wave resistance to dynamic crack propagation arises because of excitation of structure-associated waves which carry energy away from the crack tip. Two types of strucure are important: the initial, spatial structure and the surface structure (as damaged crack faces with their roughness, microcracking etc.) induced by the waves in the vicinity of the crack tip. In this context, discrete lattices and homogeneous media with a structure - media with internal degrees of freedom - are considered. In the latter case, the spatial structure is introduced by the strain-rate-dependent moduli and density. The surface structure is described by a specific dynamic condition at the crack faces. Energy release associated with the surface structure is determined. A general, structure- and crack-speed-dependent expression of the wave resistance is presented. The conditions of the existence of energy release in a 'refined' model of the medium are shown and a procedure for the proper homogenization of a structured material (to be adequate for fracture dynamics) is found.