Equilibrium of phases with interfacial energy : a variational approach

0360209 - MÚ 2012 RIV NL eng J - Journal Article
Šilhavý, Miroslav
Equilibrium of phases with interfacial energy : a variational approach.
Journal of Elasticity. Roč. 105, 1-2 (2011), s. 271-303. ISSN 0374-3535. E-ISSN 1573-2681
Institutional research plan: CEZ:AV0Z10190503
Keywords : phase transitions * phase interface * interface polyconvexity
Subject RIV: BA - General Mathematics
Impact factor: 1.110, year: 2011
http://www.springerlink.com/content/w4p16v37t032v632/

The paper proves the existence of equilibrium two phase states with elastic solid bulk phases and deformation dependent interfacial energy. The states are pairs consisting of the deformation on the body and the region occupied by one of the phases in the reference configuration. The bulk energies of the two phases are polyconvex functions representing two wells of the substance. The interfacial energy is interface polyconvex. The last notion is introduced and discussed, together with the interface quasiconvexity and interface null lagarangians. The constitutive theory and equilibrium theory of the interface are discussed in detail under appropriate smoothness hypotheses. Various forms of the interfacial stress relations for the standard and configurational (Eshelby) interfacial stresses are established. The equilibrium equations are derived by a variational argument emphasizing the roles of outer and inner variations.
Permanent Link: http://hdl.handle.net/11104/0197815