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MiS Preprint
35/2006

Normal modes and nonlinear stability behaviour of dynamic phase boundaries in elastic materials

Heinrich Freistühler and Ramón G. Plaza

Abstract

This paper considers an ideal non-thermal elastic medium described by a stored-energy function $W$. It studies time-dependent configurations with subsonically moving phase boundaries across which, in addition to the jump relations (of Rankine-Hugoniot type) expressing conservation, some kinetic rule $g$ acts as a two-sided boundary condition. The paper establishes a concise version of a normal-modes determinant that characterizes the local-in-time linear and nonlinear (in)stability of such patterns. Specific attention is given to the case where $W$ has two local minimizers $U^A,U^B$ which can coexist via a static planar phase boundary. Dynamic perturbations of such configurations being of particular interest, the paper shows that the stability behaviour of corresponding almost-static phase boundaries is uniformly controlled by an explicit expression that can be determined from derivatives of $W$ and $g$ at $U^A$ and $U^B$.

Received:
Mar 29, 2006
Published:
Mar 29, 2006
Keywords:
phase boundaries, Lopatinski determinant

Related publications

inJournal
2007 Repository Open Access
Heinrich Freistühler and Ramon G. Plaza

Normal modes and nonlinear stability behaviour of dynamic phase boundaries in elastic materials

In: Archive for rational mechanics and analysis, 186 (2007) 1, pp. 1-24