Wave propagation in nonlinear and hysteretic media -- a numerical study. (Q1866308)

The authors deal with a second-order, high-resolution central scheme that is used to develop an effective and robuste computer program for the solution of problems of wavew propagation in nonlinear and hysteretic media (from which the McCall and Guyer model can be derived too). General nonlinear constitutive laws are thus presented, as well as wave propagation in nonlinear elastic media, involving the transformation into conservation form (for a quadratic stress-strain relationship), the formulation of a Riemann problem and the considering of single- and double wave number harmonic excitations. Wave propagation has been also put in evidence in case of the Duhem model of active hysteresis and analogous problems have been dealt with. Using the Kurganov-Tadmor scheme, numerical results, plotted into diagrams, have been obtained. It is shown that the consumption (loss) of the input energy as well as the intensity of the appearance of wave number combinations makes a hysteretic medium distinctly different from a nonlinear elastic medium.