Mathematical modelling of fracture waves in a blocky medium with thin compliant interlayers

Abstract

Physical mechanisms that contribute to the generation of fracture waves in condensed media under intensive dynamic impacts have not been fully studied. One of the hypotheses is that this process is associated with the blocky structure of a material. As the loading wave passes, the compliant interlayers between blocks are fractured, releasing the energy of self-balanced initial stresses in the blocks, which supports the motion of the fracture wave. We propose a new efficient numerical method for the analysis of the wave nature of the propagation of a system of cracks in thin interlayers of a blocky medium with complex rheological properties. The method is based on a variational formulation of the constitutive relations for the deformation of elastic–plastic materials, as well as the conditions for contact interaction of blocks through interlayers. We have developed a parallel computational algorithm that implements this method for supercomputers with cluster architecture. The results of the numerical simulation of the fracture wave propagation in tempered glass under the action of distributed pulse disturbances are presented. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.