Plastic propagation of band-waves in solids

Abstract

Herewith we present a thermodynamic theory of "plastic propagation" of strain bands. The theory results in a Wave equation where the time of propagation is not the Newtonian time t but the intrinsic time z (in the sense of Valanis), the increment of which is proportional to the norm of the increment of the plastic strain tensor. To our knowledge the concept of plastic propagation is new in theoretical mechanics. The equation is solved exactly for the case of a flat semi-infinite strip under axial tension. The solution depicts the propagation of bands, upon plastic extension of the strip, in the axial direction, very much in accordance with observation.