Strain localization in a continuum as an instability event

Abstract

The paper presents a novel physical model, based on perturbation theory, to describe localization pattern formation in a solid material as a result of system instabilities. Such kind of approach has been inspired by the theory of population dynamics. In particular, the sinergetic phenomenon of strain localization into a stressed continuum, and its subsequent evolution to cohesive cracking, is obtained through the competition of an external source of energy (e.g., strain energy) and of the internal behavior of the material. The hypothesis of mobile energy entities within material bulk is put forward. These entities, which under low strain conditions are evenly distributed throughout the body, can be considered as strain quanta. The quantization of mechanical quantities is not new in continuum and fracture mechanics, [see, e.g., Novozhilov (1969, Prik Mat Mek 33:212–222)]. With increasing strain, a certain critical point is reached when the homogeneous situation becomes unstable and the strain quanta begin to aggregate into bands, leading to periodic strain localization patterns. The model, which is only theoretical at this stage, can be applied to the particular case of dry snow avalanches. In these cases, snow avalanche triggering is due toinstability (onset of sliding onto a weak plane) and is controlled by external loading (e.g., weight of the slope, load by skiers) and by internal factors (e.g., temperature changes, snow phase transformations etc.).