On description of hysteretic behaviour of materials

In the paper, a modification of well known extended Masing’s rules is suggested in order to provide more flexible description of stress–strain relationships of different materials. Particularly, the modification allows us to regulate the dependence of the damping ratio on the strain amplitude in the process of cycle deforming of a material. As the four extended Masing’s rules have a good mechanical basis in models of Iwan’s type, it is appropriate to retain whenever possible the main context of these rules. The suggestion consists only in modification of the second rule, in which instead of the scaled backbone curve another function is considered. The two cases of hysteretic systems are studied: the system with limited stress when strain increases without bound, and the system with constant stiffness (linear backbone curve) into which hysteretic properties are introduced. For a number of dynamic examples, a comparison of different hysteretic models is carried out.