Mechanics of Multi-Component Media

The aim of this course is to propose a different approach which allows us to describe internal evolution processes in the material. The approach is based on usage the Euler equations and the mass balance equations containing source terms. Choosing by some means the source terms that determine the mass transfer between a moving substance and the media, we can derive the equation of state of the substance. Besides the effect of stress state on evolution processes in the material (the diffusion of impurities) taken into account by introduction to the basic equations of dissipative term with a coefficient depending on the spherical part of the strain tensor. Then the classical evolution equations arise as a particular case within our approach.

We propose the approach that allows us to describe internal evolution processes in the material with the help of the Euler equations and the mass balance equations containing source terms. Then it is interesting to extend the results to the models of two-component continuum. Thereby the lectures are organized in sections as follows: a mechanical two-component model of the solid of complex structure is presented in section 2. This model is used in sections 3 and 4. In section 3 we propose a mathematical model of a fluid flow in a two-dimensional nanochannel, which is caused by the motion of one of the confining walls parallel to the other static wall. The two-component model of the material, in which atomic hydrogen dissolved, is constructed in section 4.

We investigate the influence of exchange mass between the components on the internal structure of the materials. The source terms determining the mass transfer between material components have been defined. As examples, structured liquids in nanochannels, metals with dissolved hydrogen have been considered.

Here is the link to the article by prof.D.Indeitsev File:Indeitsev.pdf

back to International MSc program "Advanced Dynamics of Discrete and Continuum Systems"