Ali Alriyabi, Said Hilout
Abstract:
In this article, we present the nonlinear Mecking-Lucke-Grilhe
model describing the temporal evolution for simple and
multi-instabilities of plastic deformation of stressed monocristal.
This model extends the linear problem considered in [9, 13, 14].
Using a nonlinear analysis, we present some results of existence
and stability of the solution with respect to the characteristics
of the material and the retarded times.
Numerical examples validating the theoretical results are also
investigated in this study.
Submitted July 18, 2010 Published February 15, 2011.
Math Subject Classifications: 34A34, 34D05, 34D20, 34A45.
Key Words: Mecking-Lucke-Grilhe equation; plastic deformation;
delay differential equations; characteristic equation;
dislocation; asymptotic stability.
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Ali Alriyabi Laboratoire de Mathématiques et Applications Université de Poitiers, Boulevard Marie et Pierre Curie Téléport 2, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France email: alriyabi@math.univ-poitiers.fr |
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Saïd Hilout Laboratoire de Mathématiques et Applications Université de Poitiers, Boulevard Marie et Pierre Curie Téléport 2, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France email: said.hilout@math.univ-poitiers.fr |
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