Waves in Bars of Mechanically Unstable Materials

Abstract

This paper provides an analysis of waves in thin bars made of mechanically unstable solids. The concept of a material being unstable leads to a number of experimental observations being unified. The same stress-strain relation is used for very slow rates of unloading and for impact phenomena. In particular, incremental strain waves in the unstable material are predicted to travel at the elastic-bar velocity, because the stress-strain relation usually has a local slope equal to the Young’s modulus even in the plastic range of deformation. At certain discrete stresses, strain waves are predicted to propagate very slowly and as shock waves. Both of these results agree with experimental data obtained from annealed aluminum. A sample of the slowly propagating wave is included. It is also shown that the propagation speed in the unstable material depends on the imposed boundary conditions even though no strain-rate effect is included in the constitutive equation.