Phase transitions with interfacial energy: convexity conditions and the existence of minimizers

0349641 - MÚ 2011 RIV AT eng C - Conference Paper (international conference)
Šilhavý, Miroslav
Phase transitions with interfacial energy: convexity conditions and the existence of minimizers.
Poly-, Quasi- and Rank-One Convexity in Applied Mechanics. Wien: Springer, 2010 - (Schröder, J.; Neff, P.), s. 177-240. CISM Courses and Lectures, vol.156. ISBN 978-3-7091-0173-5.
[CISM Course on Poly-, Quasi- and Rank-One Convexity in Applied Mechanics. Udine (IT), 24.09.2007-28.09.2007]
Institutional research plan: CEZ:AV0Z10190503
Keywords : phase intefaces * interface quasiconvexity * Eshelby tensor * rectifiable current * semiellipticity
Subject RIV: BA - General Mathematics
http://link.springer.com/chapter/10.1007%2F978-3-7091-0174-2_6

The article presents a variational theory of sharp phase interfaces bearing a deformation dependent energy. The theory involves both the standard and Eshelby stresses. The constitutive theory is outlined including the symmetry considerations and some particular cases. The existence of phase equilibria is proved based on appropriate convexity properties of the interfacial energy. Some generalization of the convexity properties is given and a relationship established to the semiellipticity condition from the theory of parametric integrals over rectifiable currents.
Permanent Link: http://hdl.handle.net/11104/0189825