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A new model of strain localization and damage band formation, inspired by population dynamics, is introduced in this paper. The basic assumption is that strain at nanoscales can be described by means of a kinetic model of molecular interaction. The strain energy induced by external sources concentrates at a numerable set of mobile entities, hereby called “strainions”. Under normal conditions these strain energy accumulators are uniformly distributed within the body. If the energy level between some molecules increases too sharply, for instance due to increasing strains, the strainions begin to dissipate heat energy and strain localization may occur. By coupling the Fick’s law for diffusion and a classical conservation law for heat production, the random motion of heat energy can be modelled. A number of physical parameters are introduced in the model. These are a proportionality constant k that measures the strength of heat attraction (called the “thermotaxis” coefficient), a “motility” constant c, and a diffusion constant D. A differential system of two nonlinear equations is obtained, which admits the uniform solution, corresponding to the equilibrium state. Then, we investigate, through the method of small perturbations, if a sudden small disturbance to the uniform state remains local and extinguishes, or propagates in space and time, leading to strain localization and damage. We found that strain localization occurs if the motility c of the strainions or
the decay rate of the heat concentration are small or, inversely, if the rate of heat production or the thermotaxis coefficient k are large.