Modeling of Processes in Structurally Nonlinear Media with Relaxation

A mechanism of nonlinear acoustic relaxation in structured media (slow time) is suggested which is based on the inter-grain contacts and the Arrhenius law for the potential barrier energy. This model results in a logarithmic relaxation law for sound velocity and the frequency of nonlinear resonance in samples of different materials. Estimates of a characteristic volume of interacting contacts give close numbers for the variety of consolidated materials, and, as expected, larger values for non-consolidated media and shear deformations. For weak (linear) waves and oscillations, the log relaxation occurs if, along the thermodynamic effects, a classical quadratic nonlinearity is also present.