Hysteresis and precondition of the standard viscoelastic solid model

In this paper, hysteresis and precondition of the standard viscoelastic solid model are studied. Based on the Boltzmann superposition principle, energy dissipation Wn+1Wn+1 of the model under two kinds of strain loadings for any complete (n+1)(n+1)th cycle is obtained. Analytic formulae for the stress difference at same strain values in the same cycle, stress difference and energy dissipation difference between any two adjacent cycles are given, and their monotonicity and limits are discussed. The results imply that the width and energy dissipation for any full cycle decrease with an increase of the period and converge to a positive constant, and provide a wonderful interpretation for hysteresis and precondition of the viscoelastic solid model from a mathematical perspective.