Defect mechanics is a rather ill-defined topic. The goal is to model the onset and propagation of a variety of defects in a solid at the macroscopic level.
Starting with a simplistic 1-d model, I will introduce the fuzzy notion of damage, a source of bad models and suspicious regularizations. Nevertheless those can generate, after proper calibration, models with sharp interfaces which can in turn be viewed as adequate first representations of fracture. Their numerical implementation, similarly suspicious, allows confrontation with experiments.
I will then conclude by considering elasto-plasticity — the solid equivalent of incompressible viscous behavior — and demonstrating that it is of a similar vein, although favored by convexity. Nevertheless, the issue of uniqueness in elasto-plasticity is as vexing as it is for Euler or Navier Stokes.
