Hysteresis in kinking nonlinear elastic solids and the Preisach-Mayergoyz model

Abstract

Herein we show that the stress-induced, dislocation-based, elastic hysteric loops of kinking nonlinear elastic solids---polycrystalline cobalt, $10\text{ }\text{vol}\text{ }\mathrm{%}$ porous ${\text{Ti}}_{2}\text{AlC}$, and fully dense ${\text{Ti}}_{3}{\text{SiC}}_{2}$---obey the scalar Preisach-Mayergoyz phenomenological model because they exhibit wiping out and congruency, two necessary and sufficient tenets of the model. We also demonstrate the power of the model in predicting the response of these materials to complex stress histories, as well as, determining the distributions of the threshold and friction stresses associated with the incipient kink bands---the fundamental microscopic units responsible for kinking nonlinear elasticity.