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Type of Publication: | Journal article |
Publication status: | Published |
Author: | Freistühler, Heinrich; Plaza, Ramón G. |
Year of publication: | 2007 |
Published in: | Archive for Rational Mechanics and Analysis ; 186 (2007), 1. - pp. 1-24. - ISSN 0003-9527. - eISSN 1432-0673 |
DOI (citable link): | https://dx.doi.org/10.1007/s00205-007-0051-y |
Summary: |
This paper considers an ideal nonthermal 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 UA,UB which can coexist via a static planar phase boundary. Being dynamic perturbations of such interesting configurations, this 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 UA and UB.
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Subject (DDC): | 510 Mathematics |
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FREISTÜHLER, Heinrich, Ramón G. PLAZA, 2007. Normal Modes and Nonlinear Stability Behaviour of Dynamic Phase Boundaries in Elastic Materials. In: Archive for Rational Mechanics and Analysis. 186(1), pp. 1-24. ISSN 0003-9527. eISSN 1432-0673. Available under: doi: 10.1007/s00205-007-0051-y
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