Abstract
The transition from a statistically homogeneous to a heterogeneous strain field is one of the frequently considered and often poorly understood intrinsic failure modes in damage tolerant materials with a disordered microstructure and inferior cohesive (fracture) strength. This type of transition occurs in brittle materials, such as rocks and concrete, primarily but not exclusively in the absence of long range tensile principal stresses. Numerous analytical and experimental studies were focused on the purely phenomenological, deterministic and continuum aspects of the deformation of a laterally confined cylindrical specimen subjected to the axial compression. At the same time the stochastic aspects of the problem and the effect that the disordered micro-structure of the material has on the localization have been only occasionally subjected to scrutiny. Similar failure modes may also take place in brittle materials subjected to high velocity impacts or random fluctuations of temperature. The focus of this short study is to highlight the non-deterministic aspects of the localization phenomenon using the methods of the statistical physics. At the current stage of this research program only the two-dimensional models were considered. Hence, the derived conclusions are largely of a qualitative nature.
