The evolution of shock waves in a viscoplastic bar with variable section

This paper discusses the propagation of one-dimensional stress waves in a viscoplastic bar with variable section. Based on the constitutive relation theory which includes internal variables, combining with the characteristic relations and the jump conditions across a shock wave, the evolution rules, indudins their differential equations and the analytical expressions, are obtained. For examples, the shock wave evolution rules in bars with Bodner and Johnson-Cook materials and different section-varying forms are discussed. The propagation rules and characteristics of stress waves behind the shock front are also calculated and discussed.