Abstract
A simple one dimensional variational model designed to mimic bulk and surface energy effects which govern the shape of some phase boundaries in crystals provides nontrivial periodic solutions which may have arbitrarily small period. These solutions are stable (unstable) when the corresponding period is sufficiently large (small), and the critical period measures the ratio of surface energy to bulk energy.
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References
Ball, J. M.; James, R. D.: Fine phase mixtures as minimizers of energy. Arch. Ration. Mech. Anal. 100 (1987) 13–52.
Carr, J.; Gurtin, M. E.; Slemrod, M.: One dimensional structured phase transformations under prescribed loads. J. Elasticity 15 (1985) 133–142
Fonseca, I.: Interfacial energy and the Maxwell rule. To appear in Arch. Ration. Mech. Anal.
Herring, C.: Some theorems on the free energies of crystal surfaces. Phys. Rev. 82 (1951) 87–93
Parry, G. P.: On shear bands in unloaded crystals. J. Mech. Phys. Solids 35 (1987) 367–382
Stuart, C. A.: Differential equations with discontinuous non-linearities. Arch. Ration. Mech. Anal. 63 (1976) 59–75
Synge, J. L.; Griffith, B. A.: Principles of mechanics (3rd edn.) McGraw Hill Book Company Ltd. New York 1959
Stuart, C. A.; Toland, J. F.: A variational method for boundary value problems with discontinuous nonlinearities. J. London Math. Soc. (2) 21 (1980) 319–328
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Parry, G.P. Stable periodic phase boundaries in unloaded crystals. Continuum Mech. Thermodyn 1, 305–314 (1989). https://doi.org/10.1007/BF01125779
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DOI: https://doi.org/10.1007/BF01125779