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The homogenized equations of motion for an activated elastic lamination in plane strain
Author(s) -
Sanguinet W.C.
Publication year - 2011
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.201000208
Subject(s) - isotropy , classical mechanics , equations of motion , mechanics , physics , plane (geometry) , stiffness , fictitious force , stress (linguistics) , mathematical analysis , mathematics , geometry , optics , thermodynamics , linguistics , philosophy
The equations of motion for an elastic laminar spatial‐temporal composite are investigated. It is assumed that the composite is binary, that is, it is assembled of two original constituents capable of changing (in space‐time) their material density, as well as their material stiffness. The condition of plane strain was then imposed on the composite. The paper begins by attempting to evaluate the materials' average Lagrangian (action density). In doing so, it immediately becomes apparent that expressions are needed for average momentum and stress. Both quantities are found to depend linearly on average strain and average velocity. After calculating the general Euler equations of motion, isotropy was assumed, and two additional forces (one being of a Coriolis nature) were found in the averaged equations of elastodynamics due to the presence of simultaneous change in both inertial and elastic properties of the original material constituents. The appearance of these two forces is a consequence of both dynamics and plane strain; the Coriolis type force disappears in the case of one dimensional strain that arises when longitudinal dynamic disturbances propagate along an elastic bar.