Abstract
Mathematical models of the linear elasticity and viscoelastic problem for capillary-porous materials with fractal structure is constructed. The basic physical and geometric relationships of the stress-strain state of the considered material are obtained. Integro-differentiation apparatus of fractional order to account the fractal structure of the material was used. The fractal integral relations for determining the components of the stress vector due to deformation were obtained. A variational formulation of the linear elasticity and viscoelasticity deformation problems for capillary-porous materials with fractal structure was constructed. That allows to obtain a a continuous solution of the problems that takes into account the fractal structure of the material. A method for getting an approximate solution for the considered problem is proposed. For partial cases the numerical solutions of this problems was obtained are analyzed. The dependence of stress components on the degree of material fractality was analyzed. The obtained results indicate that with increasing the degree of material fractality the absolute values of the stress components increase.
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Shymanskyi, V., Sokolovskyy, Y. (2021). Variational Formulation of Viscoelastic Deformation Problem in Capillary-Porous Materials with Fractal Structure. In: Shakhovska, N., Medykovskyy, M.O. (eds) Advances in Intelligent Systems and Computing V. CSIT 2020. Advances in Intelligent Systems and Computing, vol 1293. Springer, Cham. https://doi.org/10.1007/978-3-030-63270-0_44
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