Geodesic
Calculation of deformations in nanocomposites using the block multipole method with the analytical-numerical account of the scale effects
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1302-1321

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Local scale effects for linear continuous media are investigated as applied to the composites reinforced by nanoparticles. A mathematical model of the interphase layer is proposed that describes the specific nature of deformations in the neighborhood of the interface between different phases in an inhomogeneous material. The characteristic length of the interphase layer is determined formally in terms of the parameters of the mathematical model. The local stress state in the neighborhood of the phase boundaries in the interphase layer is examined. This stress can cause a significant change of the integral macromechanical characteristics of the material as a whole if the interphase boundaries are long. Such a situation is observed in composite materials reinforced by microparticles and nanoparticles even when the volume concentration of the inclusions is small. A numerical simulation of the stress state is performed on the basis of the block analytical-numerical multipole method with regard for the local effects related to the special nature of the deformation of the interphase layer in the vicinity of the interface. 
@article{ZVMMF_2006_46_7_a14,
     author = {D. B. Volkov-Bogorodskii and Yu. G. Evtushenko and V. I. Zubov and S. A. Lur'e},
     title = {Calculation of deformations in nanocomposites using the block multipole method with the analytical-numerical account of the scale effects},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1302--1321},
     publisher = {mathdoc},
     volume = {46},
     number = {7},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a14/}
}
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D. B. Volkov-Bogorodskii; Yu. G. Evtushenko; V. I. Zubov; S. A. Lur'e. Calculation of deformations in nanocomposites using the block multipole method with the analytical-numerical account of the scale effects. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1302-1321. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a14/