ACCELERATION-WAVES IN FINITELY DEFORMED ELASTIC-PLASTIC SOLIDS

Conditions under which acceleration waves may propagate in elastic-plastic solids undergoing finite deformations, are studied. The constitutive theory employed incorporates models corresponding to yield surfaces with vertices. Three types of acceleration wave are considered, according to whether the regions ahead and behind the wavefront are loading plastically or unloading elastically. For the case of smooth yield surfaces it is shown that wave speeds for elastic-plastic materials are bounded on either side by corresponding elastic wave speeds; these are what are generally known as Mandel's inequalities. Principal waves are investigated for the case of smooth and nonsmooth yield surfaces, and for an elastically isotropic but otherwise arbitrary material. The propagation condition for transverse waves is independent of plastic behaviour, while the condition for longitudinal waves incorporates the plastic state of the material in a simple way. Finally, the wave speeds corresponding to longitudinal waves propagating in a material which is in a state of uniaxial stress, are considered for the case of the von Mises and Tresca yield conditions, and in the case of the Tresca condition, for an isotropic hardening law which incorporates coupling between two distinct active yield surfaces. A simple bound on the coupling constant dictates which of the two wave speeds (von Mises or Tresca) is larger.