The propagation of impact-induced tensile waves in a kind of phase-transforming materials

This paper concerns the propagation of impact-generated tensile waves in a one-dimensional bar made of a kind of phase-transforming materials, for which the stress–strain curve changes from concave to convex as the strain increases. We use the fully nonlinear curve instead of approximating it by a tri-linear curve as often used in literature. The governing system of partial differential equations is quasi-linear and hyperbolic–elliptic. It is well known that the standard form of the initial-boundary value problem corresponding to impact is not well-posed at all levels of loading. In this paper, we describe in detail the propagation of impact-induced tensile waves for all levels. In particular, by means of the uniqueness condition on phase boundary derived recently, we construct a physical solution of the initial-boundary value problem mentioned above, and analyze the geometrical structure and behavior of the physical solution.