Stress-strain state modeling of a thermoelastic diffusion layer


Аuthors

Davydov S. A.1, Zemskov A. V.2*

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. ,

*e-mail: azemskov1975@mail.ru

Abstract

The materials creation with pre-programmed properties and their modification to new quali- ty standards is one of the actual development areas in the field of processing technology for structural materials. The development of mathematical models of the impact of various factors on the processed material and the analysis of the results obtained allow us to consider a larger number of exposure options while minimizing financial costs in complex high-tech processes. There are a number of approaches to the creation of mathematical models, and one of the pro- mising ones, which makes it possible to most accurately analytically describe the process under consideration, is the construction of coupled field models, an example of which is thermome- chanical diffusion. The thermomechanical diffusion model is a description of the interaction of the fields of temperature, displacement, and concentrations. We consider an algorithm for sol- ving the unsteady dynamic problem of thermoelastic diffusion perturbations propagation in a multicomponent isotropic layer. One-dimensional physical and mechanical processes in the me- dium are described by the locally-equilibrium model, which includes the equations of elastic medium motion, heat transfer, and mass transfer. The unknown functions are sought in the inte- gral form, which is a convolution in time of the Green’s functions and the boundary conditions. The effects of cross diffusion and nonzero relaxation times are taken into account. To find the Green’s functions, the Laplace transform in time and Fourier series expansion in spatial coordi- nate are used. The analysis of the obtained Green functions is done. Test calculation is conducted.

Keywords:

thermoelastic diffusion, Green's function, integral transformation, multicomponent medium, unsteady problem.

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