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

Dai, Huihui; Kong, Dexing

IMA J. Appl. Math. 71, No. 1, 14-33 (2006).

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.

MSC:

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

Keywords:

kinetic relations

Citations:

Zbl 1041.74010