A novel family of multiple springs models suitable for biaxial rate-independent hysteretic behavior

This paper presents a novel family of multiple springs models capable of reproducing the nonlinear response typical of mechanical systems and materials having a biaxial kinematic rate-independent hysteretic behavior. In such a formulation, the generalized force vector, representing the output variable, is computed by summing the contribution of n springs, respectively made up of a nonlinear elastic spring in parallel with a rate-independent hysteretic one. In particular, the generalized force of each spring is computed as a function of the related generalized displacement and history variable. Two isotropic biaxial hysteretic models are derived from the proposed general formulation: the Multiple Springs Bilinear Model and the Multiple Springs Exponential Model. The former is an algebraic model that is illustrated to clearly explain the meaning of the parameters and variables adopted in the formulation. Conversely, the latter is a transcendental model that is presented not only to demonstrate the potentiality of the family in terms of accuracy and computational efficiency, but also to show the possibility of developing models that can reproduce different types of biaxial hysteretic behavior with few parameters having a clear mechanical significance. Such a sophisticated model is validated through numerical and experimental tests.