Failure can occur in many distinctly different ways depending on the material, stress and strain fields, temperature field, environmental effects, strain rate, etc. The proposed research program will focus on a single well defined class of failure modes common to many structures and machine elements. This class of problems is characterized by a gradually evolving microscale process which at a certain point triggers a discontinuous or singular (qualitative) change of macroscale response. Consideration of critical states of cooperative processes requires radical departure from the well traveled paths. Recently developing methods of statistical physics seem to be applicable to the class of problems under consideration. These models are generally formulated as discrete enabling consideration of spatial-temporal complexities as they raise from the microstructural disorder. However, in many cases these models in the limit do not converge to the traditional continuum theories.