Abstract
In order to understand how the macroscopic stress-strain properties of metallic materials are caused by their microscopic structures, we mathematically analyze a microscopic model which describes the dynamics of the materials by applying the theory of soliton system. We treat the typical atomic chain model which includes topological defects and consists of the thermal effect, the interactions of atoms, the friction from the environment and the external force. Moreover, we extend the chain model as a microscopic model by considering the effects of work hardening and internal friction. The dynamics of the microscopic model are given by the extended thermal overdamped sine-Gordon equation and a coupled equation. Solving the pair of equations by the perturbation expansion, we derive the macroscopic stress-strain response. In the static case, we show that inelastic behavior is displayed by the microscopic model and that it is derived from the effects of work hardening and internal friction. In the dynamic case, the shape of the hysteresis loop obtained by the microscopic model qualitatively corresponds to well-known experimental data better than that of the typical rheological model. We analytically show the effect of the work hardening and the interal friction on the hysteresis loop.
