On the Asympotic Analysis of Travelling Shocks and Phase Boundaries in Elastic Bars,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
This investigation is concerned with the propagation of shocks and phase boundaries in elastic solids. Attention is restricted to one-dimensional motions for simplicity, imagine a bar in which transverse displacements are absent. The problem is introduced in section II, where it is reviewed how change of phase phenomena can be modelled by means of a nonmonotonic stress-strain law. This section also treats the simple wave that develops whenever a nonzero load delta infinity is suddenly applied to the end of the bar. This simple wave would be expected to mirror in some fashion the ultimate state of affairs whenever the bar is gradually loaded at one end of the level delta infinity provided waves are not subsequently reflected back from the opposite end. Issues involved in such an asymptotic study are discussed in the third section. Section IV addresses special considerations for materials in which the stress-strain law is piecewise linear. Then, in section V, the author carries out an asymptotic analysis for an example problem involving such a material.