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A sharp interface evolutionary model for shape memory alloys
Author(s) -
Knüpfer Hans,
Kružík Martin
Publication year - 2016
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.201500209
Subject(s) - quasistatic process , interface (matter) , orientation (vector space) , boundary (topology) , shape memory alloy , microstructure , phase (matter) , elastic energy , deformation (meteorology) , materials science , statistical physics , mechanics , geometry , classical mechanics , computer science , physics , mathematical analysis , mathematics , thermodynamics , composite material , bubble , quantum mechanics , maximum bubble pressure method
We show the existence of an energetic solution to a quasistatic evolutionary model of shape memory alloys. Elastic behavior of each material phase/variant is described by polyconvex energy density. Additionally, to every phase boundary, there is an interface‐polyconvex energy assigned, introduced by M. Šilhavý in [49][M. Šilhavý, 2010]. The model considers internal variables describing the evolving spatial arrangement of the material phases and a deformation mapping with its first‐order gradients. It allows for injectivity and orientation‐preservation of deformations. Moreover, the resulting material microstructures have finite length scales.