Executive Summary : | Dynamic fracture propagation at a planar interface between elastic solids has been extensively studied in the literature. Non-planarity of the interface introduces coupling of the fracture modes and is less well studied. It is proposed to develop new numerical schemes for the study of non-planar dynamic fractures under 2D antiplane strain and plane strain conditions. The numerical schemes will be based on the boundary integral equation method. This method relates the displacement discontinuity at an interface to the tractions acting on the interface. The advantage of the method is that it involves stresses and displacements only on the interface and field quantities away from that interface need not be evaluated. In the literature, boundary integral equation based numerical methods have done the elastodynamic space-time convolution of the displacement discontinuity at the interface. It is proposed to introduce a new approach involving the space-time convolution of the tractions at the interface. The boundary integral equation is then coupled with a constitutive law for the interface. This closed set of equations giving rise to a mixed boundary value problem can be solved numerically to model spontaneous dynamic fracture propagation. The key feature of the approach is that it is based on exact elastodynamic principles and there are no ad-hoc assumptions made on the fracture initiation or propagation. The numerical schemes developed here are expected to be of useful for mechanical engineering and geophysical applications. |