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Normal Modes and Nonlinear Stability Behaviour of Dynamic Phase Boundaries in Elastic Materials

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2007

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Plaza, Ramón G.

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https://doi.org/10.1007/s00205-007-0051-y
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Archive for Rational Mechanics and Analysis. 2007, 186(1), pp. 1-24. ISSN 0003-9527. eISSN 1432-0673. Available under: doi: 10.1007/s00205-007-0051-y

Zusammenfassung

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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510 Mathematik

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ISO 690FREISTÜHLER, 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. 2007, 186(1), pp. 1-24. ISSN 0003-9527. eISSN 1432-0673. Available under: doi: 10.1007/s00205-007-0051-y
BibTex
@article{Freistuhler2007-09-10Norma-40758,
  year={2007},
  doi={10.1007/s00205-007-0051-y},
  title={Normal Modes and Nonlinear Stability Behaviour of Dynamic Phase Boundaries in Elastic Materials},
  number={1},
  volume={186},
  issn={0003-9527},
  journal={Archive for Rational Mechanics and Analysis},
  pages={1--24},
  author={Freistühler, Heinrich and Plaza, Ramón G.}
}
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