Some Wave Propagation Problems in Plastic-viscoplastic Materials

Lubliner suggested that the uniaxial constitutive equation (1.1) be used in the numerical solution of wave-propagation problems, and that the results approximating those of either hypothesis may be obtained in extreme cases. He further showed on the basis of an extremely simple, piece-wise linear, model of plastic-viscoplastic behavior, that results approaching the viscoplastic hypothesis will be obtained under one or more of the following circumstances: (1) weak impact, (2) long bar, (3) short 'relaxation' time (or natural time of the material); that converse conditions will lead to results approaching the plastic hypothesis; and that intermediate conditions require the use of the general constitutive equation. The purpose of the present study is to test further the validity of Lubliner's suggestions by means of numerical solutions of representative wave-propagation problems in bars whose mechanical behavior is described by the uniaxial constitutive equation, slightly modified to account for loading-unloading behavior.