Wave Propagation in a Strain‐Softening Bar:Exact Solution

Abstract

A closed‐form solution is given for a one‐dimensional bar which undergoes strain strain softening., a gradual decline of stress to zero at increasing strain). It is shown that strain softening can occur in the interior of a body, and that The length of the strain‐softening region tends to localize into a point, which agrees with what was previously shown by stability analysis for static situations. The stress in the strain‐softening cross section drops to zero instantly, regardless of the shape of the strain‐softening diagram, and the total energy dissipated in the strain‐softening domain of the bar is found to vanish. Despite these unpleasant features, the problem apparently possesses a solution for certain boundary and initial conditions. However, the fact that the energy dissipation in the strain‐softening process vanishes is not representative of the experimentally observed behavior of real strain‐softening materials such as concrete or geomaterials.