Impact of a finite elastic-viscoplastic bar

Abstract

A method for predicting the response of strain-rate sensitive structures under dynamic loading is developed. It is based on a finite difference method, the incremental theory of plasticity, and an elastic work-hardening viscoplastic material idealization. The strain-rate effect, loading and unloading conditions, and wave interactions are automatically accounted for, and adjusted if necessary, as the deformation proceeds. No iteration is required even if the field equations are nonlinear (e.g. non-linear constitutive equations, large deformation, or complicated geometry). We solve as an example the small deflection of a finite bar with a concentrated tip mass. The accuracy is comparable to that obtained by the well-known method of characteristics, a powerful tool for solving elastic-viscoplastic wave problems but which is restricted to small deflections and simple geometry. Because of the form of the constitutive relation selected (elastic work-hardening visco-plastic), several important new features of the dynamics response are brought out. These features are not revealed when simpler, computationally-convenient constitutive relations, such as rigid ideal-viscoplastic, rigid work-hardening viscoplastic and elastic ideal-viscoplastic are used.