Abstract
This paper discusses some recent work with M. Gurtin and M. Slemrod on the displacement boundary value problem of a one-dimensional elastic material capable of exhibiting exchanges of phase. This study was motivated by some work of Ericksen [4], who showed that by taking a non-convex stress strain law, elasticity could model phase changes (see also Antman [2], and Antman and Carbone [3]).
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References
Andrews, G., and Ball, J.M.: 1982, Asymptotic behaviour and changes of phase in one-dimensional viscoelasticity, J. Differential Equations 44, pp. 306–341.
Antman, S.S.: 1973, Nonuniqueness of equilibrium states for bars in tension, J. Math. Anal. Appl. 44, pp. 333–349.
Antman, S.S., and Carbone, E.R.: 1977, Shear and necking instabilities in nonlinear elasticity, J. Elasticity 7, pp. 125–151.
Ericksen, J.L.: 1975, Equilibrium of bars, J. Elasticity 5, pp. 191–201.
James, R.D.: 1979, Co-existent phases in the one-dimensional static theory of elastic bars, Arch. Rational Mech. Anal. 77, pp. 99–140.
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© 1983 D. Reidel Publishing Company
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Carr, J. (1983). Phase Transitions via Bifurcation from Heteroclinic Orbits. In: Ball, J.M. (eds) Systems of Nonlinear Partial Differential Equations. NATO Science Series C: (closed), vol 111. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7189-9_19
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DOI: https://doi.org/10.1007/978-94-009-7189-9_19
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