The propagation of high frequency, finite acceleration pulses and shocks in viscoelastic materials

Abstract

The modes of propagation of one dimensional, finite amplitude, high frequency pulses in viscoelastic (rate dependent) materials is discussed in detail. Shock formation and shock propagation, together with conditions under which the model can be approximated to by an elastic model, are emphasized. Whereas the elastic model predicts shock formation at a wavelet if β , the ratio of induced acceleration to a natural acceleration defined by the material, is positive, the viscoelastic model predicts shock formation only when β > 1. Linear and nonlinear elastic behaviour are approached in the limits | β | → 0 and | β |→ ∞ respectively, over distances which are small compared with a characteristic relaxation distance. For intermediate values of β conditions at a wavelet differ from those predicted by an elastic model. The expansion techniques described are also applicable to the equations governing the behaviours of nonlinear transmission lines.