Geodesic
Mathematical modelling of deformation of porous organic materials
Journal of computational and engineering mathematics, Tome 9 (2022) no. 4, pp. 34-43.

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In this paper, we propose a method to describe the dynamics of deformation of polymeric materials under thermal and mechanical impacts. The method is based on solving the equation for a viscous incompressible fluid in the quasi-stationary approximation. This method is implemented for the case of simple compression of a cylindrical sample, the thickness of which is much less than its diameter. We construct dependencies of the viscosity coefficient on temperature and determine the relaxation time for the Maxwell mathematical model. It is shown that the viscosity of materials strongly depends on temperature, and this dependence is exponential. The performed calculations of the deformation of various polymeric materials demonstrate satisfactory agreement with the experimental data over the entire temperature range.
Keywords: viscous incompressible fluid, Maxwell mathematical model, heat conduction, equation of state. 
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     title = {Mathematical modelling of deformation of porous organic materials},
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A. A. Aiderkhanova; Yu. M. Kovalev; A. P. Yalovets. Mathematical modelling of deformation of porous organic materials. Journal of computational and engineering mathematics, Tome 9 (2022) no. 4, pp. 34-43. http://geodesic.mathdoc.fr/item/JCEM_2022_9_4_a3/