Global structure stability of impact-induced tensile waves in a rubber-like material. (English) Zbl 1114.74024

Summary: This paper concerns the global structure stability of impact-generated tensile waves in a one-dimensional 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 nonlinear’ so that the standard form of initial-boundary value problem corresponding to impact is not well-posed at all levels of loading. However, J. K. Knowles [SIAM J. Appl. Math. 62, 1153–1175 (2002; Zbl 1041.74010)] 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.


74H55 Stability of dynamical problems in solid mechanics
74J40 Shocks and related discontinuities in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74M20 Impact in solid mechanics


Zbl 1041.74010
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