Damage and self-similarity in fracture

Consider applications of damage mechanics to material failure. The damage variable introduced in damage mechanics quantifies the deviation of a brittle solid from linear elasticity. An analogy between the metastable behavior of a stressed brittle solid and the metastable behavior of a superheated liquid is established. The nucleation of microcracks is analogous to the nucleation of bubbles in the superheated liquid. In this paper we have applied damage mechanics to four problems. The first is the instantaneous application of a constant stress to a brittle solid. The results are verified by applying them to studies of the rupture of chipboard and fiberglass panels. We then obtain a solution for the evolution of damage after the instantaneous application of a constant strain. It is shown that the subsequent stress relaxation can reproduce the modified Omori’s law for the temporal decay of aftershocks following an earthquake. Obtained also are the solutions for application of constant rates of stress and strain. A fundamental question is the cause of the time delay associated with damage and microcracks. It is argued that the microcracks themselves cause random fluctuations similar to the thermal fluctuations associated with phase changes.