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Jump conditions and kinetic relations at moving discontinuities
Author(s) -
Berezovski A.,
Maugin G.A.
Publication year - 2010
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.200900306
Subject(s) - classification of discontinuities , jump , kinetic energy , boundary (topology) , phase boundary , phase (matter) , transformation (genetics) , phase transition , kinetic theory , limiting , mechanics , classical mechanics , mathematics , boundary value problem , bar (unit) , mathematical analysis , statistical physics , thermodynamics , physics , chemistry , quantum mechanics , mechanical engineering , biochemistry , meteorology , engineering , gene
The problem of the kinetics of moving discontinuities is described on the example of the propagating phase‐transition front that corresponds to a stress‐induced martensitic transformation in an elastic bar. The kinetic relation is derived under the assumption of a linear dependence between the stress jump at the phase boundary and the driving force. The derived kinetic relation is consistent with jump relations and satisfies limiting requirements. The comparison of the developed theory with available experimental data is made in the case of the dynamics of a straight brittle crack. The corresponding kinetic relation is derived under the same assumption as in the case of phase boundary. Classical results for Homalite‐100 as well as recent experiments for Polyester/TiO 2 are compared with the prediction of the kinetic relation. The agreement between theory and experiment is rather good, especially for such a simple theoretical model.