Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Миколайчук М.А.   Князева А.Г.  

Coupled two dimensional problem of diffusion under external loading

Reporter: Миколайчук М.А.

Two dimensional problem of one-axis loaded plate admixture saturation was considered. Mechanical part of problem was formulated under the Bernoulli-Euler hypothesis. Lateral displacements are negligible. We are supposed that axial deformation is an linear function of coordinates in the cross-sectional plane. Stresses was obtained as functions of deformations which was expressed in terms of displacements. Relation between deformations and stresses described with Duhamel–Neumann Law. In the defining relationship we have volume changing function which depends on admixture concentration. Thereby, without external loading plate stressed state depend on concentration stresses. Unknown functions from axis displacement definition was obtained from system of linear algebra equations which was written as result of conditions of equilibrium for resultant forces and torques
Two possible influence mechanisms of starins and stresses on diffusion were analyzed for diffusion part of problem. First of them related with diffusion activation energy change by lattice deformation. To relate activation energy with stress and strains, which presence in the system, we need introduce some notion, such as activation volume. Activation volume is difference between local volumes of the system in the ground and activated states. Ultima analysi, we can say that the work of stresses, which are presence in the local volume, is explicitly influence to diffusivity. We have used this diffusivity in the our model. Second mechanism consist in a mass transfer of impurity under stresses. It like pressure diffusion mass transfer in a liquids.
As result we can say that diffusion depend on sign and value of external stress. Stress influence to diffusion is more intensive at the low temperatures.
The work was carried out in the state contract 16.740.11.0122, and supported at the financial Support of grant RFBR 10-01-00034.


Abstracts file: Mikolaichuk_novosib_2011.doc
Full text file: mikolaichuk.pdf

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