Abstract
Based on the seminal works by Ball (1982) and Pericak-Spector and Spector (1988) we investigate compressible, nonlinear elastodynamics as a model describing the onset of fracture or cavitation in a softening elastic material under tensile load. We explore a definition of singular solutions describing fracture via approximating sequences of smooth functions. Moreover, we use these approximating sequences to investigate the energy of such solutions, taking into account the energy needed to open a crack or hole. In particular, we find that the existence of singular solutions and the finiteness of their energy is strongly related to the behavior of the stress response function for infinite stretching. We will detail our findings in one space dimension.