Global structure stability of impact-induced tensile waves in a rubber-like material

This paper concerns the global structure stability of impact-generated tensile waves in a 1D bar made of a rubber-like material. Because the stress–strain curve changes from concave to convex as the strain increases, the governing quasi-linear system of partial differential equations, though hyperbolic, fails to be ‘genuinely non-linear’ so that the standard form of the initial-boundary value problem corresponding to impact is not well-posed at all levels of loading. However, Knowles (2002, SIAM J. Appl. Math., 62, 1153–1175) constructed the solutions of the initial-boundary value problem corresponding to impact. Based on this, in this paper we prove the global structure stability of the impact-generated tensile waves constructed by Knowles. The method of the proof is constructive.