Impact-induced tensile waves in a kind of phase-transforming materials

Abstract

This paper concerns the global propagation of impact-induced tensile waves in a kind of phase-transforming materials. It is well-known that the governing system of partial differential equations is hyperbolic-elliptic and the initial-boundary value problem is not well-posed at all levels of loading. By making use of fully nonlinear stress-strain curve to model this material, Dai and Kong succeeded in constructing a physical solution of the above initial-boundary value problem. For the impact of intermediate range, they assumed that $\beta <3\alpha$ in the stress-response function for simplicity. In this paper, we revisit the impact problem and consider the propagation of impact-induced tensile waves for all values of the parameters $\alpha$ and $\beta$. The physical solutions for all levels of loading are obtained completely.

14 pages; 5 figures; submitted to IMA Journal of Applied Mathematics