Abstract
For interfacial interactions of “separable type” the existence is proved of stable multiphase equilibrium states minimizing the total energy. The total energy includes a deformation dependent contribution along sharp interfaces separating the phases. The second gradients of deformation do not occur; the theory is based on interfacial null Lagrangians as determined in [11, 12]. The interfacial interaction is always of separable type if the number of phases does not exceed 3; for the number of phases ≥ 4, the separable nature of the interface interaction is an assumption.
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References
Ambrosio, L., Fusco, N. and Pallara, D., Functions of Bounded Variation and Free Discontinuity Problems, Clarendon Press, Oxford, 2000.
Ball, J.M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63, 1977, 337–403.
Ball, J.M. and James, R.D., Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100, 1987, 13–52.
Ball, J.M. and James, R.D., Proposed experimental tests of a theory of fine microstructure and the two-well problem, Phil. Trans. Royal Soc. Lond. 338, 1992, 389–450.
Ball, J.M. and Mora-Corral, C., A variational model allowing both smooth and sharp phase boundaries in solids, Comm. Pure Appl. Anal. 8, 2009, 55–81.
Fonseca, I., Interfacial energy and the Maxwell rule, Arch. Rational Mech. Anal. 106, 1989, 63–95.
Gurtin, M.E., The nature of configurational forces, Arch. Rational Mech. Anal. 131, 1995, 67–100.
Gurtin, M.E. and Struthers, A., Multiphase thermomechanics with interfacial structure, 3. Evolving phase boundaries in the presence of bulk deformation, Arch. Rational Mech. Anal. 112, 1990, 97–160.
Müller, S., Tang, Q. and Yan, B.S., On a new class of elastic deformations not allowing for cavitation, Ann. Inst. H. Poincaré, Analyse non linéaire 11, 1994, 217–243.
Parry, G.P., On shear bands in unloaded crystals, J. Mech. Phys. Solids 35, 1987, 367–382.
Šilhavý, M., Phase transitions with interfacial energy: A variational approach, Preprint, Institute of Mathematics, AS CR, Prague. 2008-10-22, 2008.
Šilhavý, M., Phase transitions with interfacial energy: Convexity conditions and the existence of minimizers, Preprint, Institute of Mathematics, AS CR, Prague. 2009-2-16, 2009.
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Šilhavý, M. (2010). Phase Transitions with Interfacial Energy: Interface Null Lagrangians, Polyconvexity, and Existence. In: Hackl, K. (eds) IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials. IUTAM Bookseries, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9195-6_18
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DOI: https://doi.org/10.1007/978-90-481-9195-6_18
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