Analytical Modeling of Stress-Strain Behaviors under Static and Cyclic Conditions from a Microstructural Viewpoint

In order to understand nonlinear behaviors of stress-strain responses of metallic materials under static and cyclic conditions from the viewpoint of their microscopic structures, we theoretically investigate an analytical model by applying some mathematical techniques such as the soliton theory and the theory of nonlinear systems which develop greatly in recent years. The analytical model is based on 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. In addition, the analytical model is developed from the typical atomic chain model by including the effects which can relate with work hardening and internal friction. In the static case, we show that inelastic behavior is displayed by the analytical model. In the cyclic case, by using the analytical model, we obtain the nonlinear behavior of the hysteresis loop which qualitatively corresponds to well-known experimental data better than that of the typical model.