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On homogenization of activated laminates in 1D‐space and time
Author(s) -
Lurie K.A.
Publication year - 2009
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.200800185
Subject(s) - homogenization (climate) , compact space , upper and lower bounds , work (physics) , spacetime , mathematical analysis , energy–momentum relation , materials science , composite material , mathematics , geometry , classical mechanics , physics , thermodynamics , biodiversity , ecology , quantum mechanics , biology
In this paper, I discuss observations indicating that homogenization, in its standard version based on weak compactness, generally does not work for dynamic materials with arbitrary material geometry. A remarkable exception is represented by the spatial‐temporal laminates where such compactness can be established. For the slow (timelike) laminates, this was done in [18] with the use of energy bound. In the present work, a similar result is established for the fast (spacelike) laminates, this time with the use of momentum flux bound.