A multiplay model for rate-independent and rate-dependent hysteresis with nonlocal memory

We consider the multiplay model for hysteresis with nonlocal memory. This model consists of N mass/spring/dashpot with deadzone elements. The hysteresis map of the multiplay model is completely determined by the stiffness coefficients and widths of the gaps of the mass/spring/dashpot with deadzone elements. This multiplay model can be used to model a hysteretic system with a hysteresis map possessing the symmetry of the cyclic rotation group C₂. Parameters of the multiplay model can be determined based on the slope of the sampled hysteresis map. Once the multiplay model is determined, its inverse can be analytically computed.