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Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2009-5pp.599-608

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P.A. Belov and S.A. Lurie, "A continuum model of microheterogeneous media," J. Appl. Math. Mech. 73 (5), 599-608 (2009)
Year 2009 Volume 73 Issue 5 Pages 599-608
Title A continuum model of microheterogeneous media
Author(s) P.A. Belov (Moscow, Russia)
S.A. Lurie (Moscow, Russia, lurie@ccas.ru)
Abstract A correct model of media with a microstructure (according to Mindlin's definition), which is defined by the presence of free strains and generalizes the well-known Mindlin, Cosserat and AeroľKuvshinskii models, is proposed. The correctness of the formulation of the model is determined by using a ôkinematicö variational principle, based on a systematic formal description of the kinematics of media, formulation of the kinematic constraints for media of various complexity and the construction of the corresponding strain potential energy using a Lagrange multiplier procedure. A system of constitutive relations is established, and a consistent statement of the boundary-value problem is formulated. It is shown that the model of a medium investigated not only reflects scale effects that are similar to cohesive interactions, but also provides a basis for describing a broad spectrum of adhesive interactions. An interpretation of the physical characteristics responsible for non-classical effects is proposed in the context of an analysis of the physical aspects of the model, and a description of the spectrum of adhesion mechanical parameters is given.
Received 21 April 2008
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