Propagation of acoustic pulses in material with hysteretic nonlinearity

Evolution equations for propagation of both unipolar and bipolar acoustic p ulses are derived by using hysteretic stress-strain relationships. Hysteret ic stress-strain loops that incorporate quadratic nonlinearity are derived by applying the model of Preisach-Mayergoyz space for the characterization of structural elements in a micro-inhomogeneous material. Exact solutions o f the nonlinear evolution equations predict broadening in time and reductio n in amplitude of a unipolar finite-amplitude acoustic pulse. In contrast w ith some earlier theoretical predictions, the transformation of the pulse s hape predicted here satisfies the law of ''momentum'' conservation (the "eq uality of areas" law in nonlinear acoustics of elastic materials). A bipola r pulse of nonzero momentum first transforms during its propagation into a unipolar pulse of the same duration. This process occurs in accordance with the "momentum" conservation law and without formation of shock fronts in t he particle velocity profile. (C) 2000 Acoustical Society of America. [S000 1-4966(oo)04406-4].