Premium
Balance laws and a dissipation inequality for general constituents undergoing disarrangements and mixing
Author(s) -
Owen D.R.
Publication year - 2008
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.200800003
Subject(s) - dissipation , mixing (physics) , disjoint sets , limiting , balance (ability) , space (punctuation) , mathematics , classical mechanics , mechanics , statistical physics , law , physics , mathematical analysis , thermodynamics , computer science , quantum mechanics , mechanical engineering , political science , engineering , operating system , medicine , physical medicine and rehabilitation
Multiphase structured deformations provide a multiscale geometrical setting suitable for distinguishing among (1) separate constituents – N bodies that occupy mutually disjoint regions in space at all times and that submacroscopically may form voids or undergo slips, (2) intermingling constituents – N bodies, each of which splits into small non‐overlapping cells that may be in contact with cells of the same or of different constitutents, and (3) mixing constituents – N bodies that interpentrate by occupying overlapping regions in space. Earlier research based on multiphase structured deformations has established balance laws and a dissipation inequality for each constituent within the mixture when that constituent is an elastic body. The balance laws and dissipation inequality were obtained via a limiting argument from corresponding relations for intermingling constitutents whose motions approximate those of the mixing constituents. Here, such limiting arguments are shown to provide balance laws and a dissipation inequality for a much broader class of constituents.