The formulation of a new mathematical model of deformed viscoelastic composite is shown in the work. The method of constructing a model is based on commonality problems of determining the effective modules of inhomogeneous elastic composites and viscoelastic bodies, which demonstrate the dependence of the mechanical properties from the duration of load action. Mathematical model of hybrid efficient modules has been constructed on the superposition of expressions for known effective modules of Voigt and Reuss, Hashin and Shtrikman. The new model summarizes the properties of classical approximate approaches. We have shown that the calculations of stress-strain state with the help of new effective characteristics provide a more accurate prediction in comparison with known models.

The problem of determining the effective properties of composite materials is actual problem for deformable body mechanics. The model, proposed by Crisher for modeling effective values of the coefficient of thermal conductivity, has been considered. Modifications of this mathematical model for two-component elastic composite were built. Model of Hill-Budiansky compresses classic fork of Voigt-Reuss, if it is added by Voigt component. Expressions of hybrid effective characteristics through the use of effective Hashin-Shtrikman moduli are built. The accuracy is estimated depending on the type of modification of the effective characteristics for the calculation of the stress-strain state of bodies (two-layer shell and three-layer plate) made from composite materials. The results are compared with the exact classical solutions, and admissible concordance is achieved.

Институт теоретической и прикладной механики им. С.А. Христиановича СО РАН, Новосибирск, Россия Предложена математическая модель процесса легирования поверхности металла с помощью импульсного лазерного излучения, в которой учитывается зависимость температурного градиента поверхностного натяжения от концентрации поверхностно-активного вещества в расплаве и температуры разогрева. Проведено численное моделирование, результаты которого выявили развитие многовихревых течений, способствующих проникновению легирующего материала в глубину расплава.Ключевые слова: легирование металла, лазерное излучение, конвективный тепломассоперенос, численное моделирование A mathematical model is proposed to describe the process of surface alloying of metals by laser pulses. The model takes into account the dependence of the surface tension gradient induced by temperature on the concentration of a surface active agent in the melt and on the heating temperature. Numerical simulation reveals the probability of occurrence of multi-vortex flows that promote the penetration of the alloying material into the metal.

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