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Extended non‐linear relations of elastic shells undergoing phase transitions
Author(s) -
Pietraszkiewicz W.,
Eremeyev V.,
Konopińska V.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200610309
Subject(s) - curvilinear coordinates , phase (matter) , phase transition , position (finance) , surface (topology) , elastic energy , shell (structure) , interface (matter) , classical mechanics , physics , mathematics , mathematical analysis , mechanics , geometry , materials science , condensed matter physics , quantum mechanics , finance , bubble , maximum bubble pressure method , economics , composite material
The non‐linear theory of elastic shells undergoing phase transitions was proposed by two first authors in J. Elast. 79 , 67–86 (2004). In the present paper the theory is extended by taking into account also the elastic strain energy density of the curvilinear phase interface as well as the resultant forces and couples acting along the interface surface curve itself. All shell relations are found from the variational principle of stationary total potential energy. In particular, we derive the extended natural continuity conditions at coherent and/or incoherent surface curves modelling the phase interface. The continuity conditions allow one to establish the final position of the interface surface curve after the phase transition. The results are illustrated by an example of a phase transition in an infinite plate with a central hole.