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On the approximation of surface elasticity theory by means of phase‐field theory
Author(s) -
Lammen Henning,
Mosler Jörn
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900375
Subject(s) - elasticity (physics) , surface tension , surface (topology) , phase field models , mean field theory , field (mathematics) , mathematics , phase (matter) , materials science , physics , mathematical analysis , thermodynamics , condensed matter physics , geometry , quantum mechanics , pure mathematics
Within surface elasticity theory originally proposed by Gurtin and co‐workers ( [1]), effects associated with surface tension are naturally captured. In this paper, surface elasticity theory is approximated by means of phase field theory, cf. [4] and [5]. The resulting approximation is employed in order to analyze the size effects induced by the coupling of bulk and surface energies. For that purpose, the phase field framework is compared to the underlying sharp interface model proposed in [2].