Multi-scale effects in models of mechanics of continuums | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 8 > №1 / 2002 / Pages: 71-82

Multi-scale effects in models of mechanics of continuums

, , ,


We analyze the general structure of models of mechanics that contain physical constants of different dimensions in their governing equations and thus allow us considering the multi-scale effects. Presently, the problem of obtaining such models is of great importance because of a pronounced interest of researchers in the field of super think structures (nano-structures). These structures may be used for synthesis new materials with unique physical-mechanical properties. They may be used directly in medicine, electronics and in other applications. Now experimental studies of characteristics of nano-structures are well developed on the basis of testing equipment and technological processes. The characteristic dimension of structures is equal to several nano-meters. At that, theoretical investigations in simulation of multi-scale effects in nano-structures should be accelerated. We try to indicate the general structure of governing equations for models of mechanics accounting for multi-scale effects and to present a classification of these models. We present a comprehensive description of the kinematic part of problems of continuum mechanics. It is shown that in the general case a displacement vector may be represented in the form of decomposition including a potential component and a vortex one. Based on the analysis of kinematic relationships of a continuum considered as links when the models of a continuum are constructed with using the variational procedure, we propose a formal system of classification for multi-scale effects in the form of a family of solutions that decreases exponentially at infinity. It is demonstrated that known variants of models of a continuum taking into account the multi-scale effects correspond to the system of classification proposed.