Abstract:
This paper presents the results of mathematical and discrete modeling of linear dynamics problems for three-dimensional viscoelastic and porous elastic bodies. The employed methods and approaches are based on formulating boundary integral equations solved using boundary elements. The model of a standard viscoelastic body is employed as the viscoelastic model. The properties of porous elastic materials are described using the full Biot model with four basic functions. Examples of numerical solutions of the problems are compared with known results of solutions.
Keywords:
method of boundary integral equations, viscoelasticity, porous elastic bodies, inversion of the Laplace transform.
Citation:
L. A. Igumnov, A. V. Amenitskii, A. A. Belov, S. Yu. Litvinchuk, A. N. Petrov, “Numerical-analytic investigation of the dynamics of viscoelastic and porous elastic bodies”, Prikl. Mekh. Tekh. Fiz., 55:1 (2014), 108–114
\Bibitem{IguAmeBel14}
\by L.~A.~Igumnov, A.~V.~Amenitskii, A.~A.~Belov, S.~Yu.~Litvinchuk, A.~N.~Petrov
\paper Numerical-analytic investigation of the dynamics of viscoelastic and porous elastic bodies
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2014
\vol 55
\issue 1
\pages 108--114
\mathnet{http://mi.mathnet.ru/pmtf1106}
\elib{https://elibrary.ru/item.asp?id=21903147}
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https://www.mathnet.ru/eng/pmtf1106
https://www.mathnet.ru/eng/pmtf/v55/i1/p108
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V.I. Erofeev, A.V. Leonteva, “Plane longitudinal waves in a fluid-saturated porous medium with a nonlinear relationship between deformations and displacements of the liquid phase”, Comp. Contin. Mech., 14:1 (2021), 5
Van Thuong Nguyen, Chyanbin Hwu, “Indentation by multiple rigid punches on two-dimensional anisotropic elastic or viscoelastic solids”, International Journal of Mechanical Sciences, 178 (2020), 105595
Sergey M. Aizikovich, Vladimir I. Erofeyev, Anna V. Leonteva, Poromechanics VI, 2017, 1604
Kh. Kh. Il'yasov, A. V. Kravtsov, S. V. Kuznetsov, S. Ya. Sekerzh-Zen'kovich, “Features of acoustic waves in media with large porosity values in the framework of the Biot theory”, Acoust. Phys., 63:6 (2017), 711
L. A. Igumnov, I. P. Markov, Springer Proceedings in Physics, 175, Advanced Materials, 2016, 517
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