The state of affairs near a crack tip is very different when viewed at the different scales, say from the macroscopic to the atomic. These different appearances have intrigued solid state physicists, mechanists and material scientists for decades. Although they are physically connected, it is not obvious what roles would their mathematical relationships play? Investigations associated with scaling in size and time, evolution of material damage, multiscaling of macro-, meso- and micro-mechanics theories are presumably topics that could provide insights to the behavior of the internal structures...
