Reconstruction of residual stress field for inhomogeneous poroelastic media
UDC
539.3, 534-18Abstract
Poroelastic structures are widespread in many fields of technology, medicine and biology. Accounting for the presence of a porous skeleton and pore fluid makes it possible to describe the dynamic behavior of the environment more accurately. The presented article deals with the vibrations of inhomogeneous poroelastic media taking into account the initial stress field and the method of reconstruction for such field based on some data on the dynamic behavior of the structure. Initial or residual stresses make considerable contribution to the mechanical capacity of the bodies, and affect on the dynamic behavior. The presence of initial or residual stresses in mechanical structures significantly changes the stress-strain state for such systems and without taking into account this factor, results of simulation may greatly differ from the actual data. There are many methods for determining the initial stress fields, including the X-ray methods, techniques of scratching and drilling, as well as the method of acoustic sensing, that belongs to the nondestructive testing methods and requires a special attention. We considered the problem of reconstruction of the initial stress field for an inhomogeneous poroelastic column, which is based on acoustic sensing method. The equations for the longitudinal oscillations of poroelastic inhomogeneous body in the presence of initial stress field are formulated. The influence of the level of initial stress and Biot modulus on the dynamic behavior of medium is studied. A series of numerical experiments on the reconstruction of various distribution laws for initial stress field are performed.
Keywords:
poroelasticity, initial stress, reconstruction of inhomogeneous characteristics, vibrationFunding information
Работа выполнена при поддержке государственного задания Минобрнауки России (9.665.2014/K) и РФФИ (14-01-31453 мол_а, 13-01-00196).
References
- Ватульян А.О., Дударев В.В., Недин Р.Д. Предварительные напряжения: моделирование и идентификация. Ростов-на-Дону: Издательство Южного федерального университета, 2014. 206 с. [Vatul'yan A.O., Dudarev V.V., Nedin R.D. Predvaritel'nye napryazheniya: modelirovanie i identifikatsiya [Prestressing: modeling and identification]. Rostov-on-Don, Izdatel'stvo Yuzhnogo federal'nogo universiteta Publ., 2014, 206 p. (In Russian)]
- Тихонов А.Н., Арсенин В.Я. Методы решения некорректных задач. М.: Наука, 1979. 285 с. [Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnykh zadach [Methods of solving ill-posed problems]. Moscow, Nauka Publ., 1979, 285 p. (In Russian)]
- Ватульян А.О. К теории обратных коэффициентных задач в линейной механике деформируемого тела // ПММ. 2010. Т. 74. № 6. С. 911-918. [Vatul'yan A.O. K teorii obratnykh koeffitsientnykh zadach v lineynoy mekhanike deformiruemogo tela [On the theory of inverse problems in the linear solid mechanics]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics], 2010, vol. 74, no. 6, pp. 911-918. (In Russian)]
- Ватульян А.О. О вариационной постановке обратных коэффициентных задач для упругих тел // ДАН. 2008. Т. 422. № 2. С. 182-184. [Vatul'yan A.O. O variatsionnoy postanovke obratnykh koeffitsientnykh zadach dlya uprugikh tel [On the variational formulation of inverse problems for elastic bodies]. Doklady Akademii nauk [Rep. of Russian Academy of Sciences], 2008, vol. 422, no. 2, pp. 182-184. (In Russian)]
- Ватульян А.О. Обратные задачи в механике деформируемых твердых тел. М.: Физматлит, 2007. 223 c. [Vatul'yan A.O. Obratnye zadachi v mekhanike deformiruemykh tverdykh tel [Inverse problems in the mechanics of deformable solids]. Moscow, Fizmatlit Publ., 2007, 223 p. (In Russian)]
- Kiani K., Avili H.G., Kojorian A.N. On the role of shear deformation in dynamic behavior of a fully saturated poroelastic beam traversed by a moving load // International Journal of Mechanical Sciences. 2015. Vol. 94. P. 84-95.
- Van der Kelen C., Cuenca J., Goransson P. A method for the inverse estimation of the static elastic compressional moduli of anisotropic poroelastic foams - With application to a melamine foam // Polymer Testing. 2015. Vol. 43. P. 123-130.
- Ilango S.J.J., Sarkar S., Sameen A. Reconstruction of 2-D porous media using Karhunen–Lo'eve expansion // Probabilistic Engineering Mechanics. 2012. Vol. 32. P. 56-65.
- Chung Sang-Yeop, Han Tong-Seok, Kim Se-Yun, Lee Tae-Hyung Investigation of the permeability of porous concrete reconstructed using probabilistic description methods // Construction and Building Materials. 2012. Vol. 66. P. 760-770.
- Wang Qinghui, Huang Xiang, Zhou Wei, Li Jingrong Three-dimensional reconstruction and morphologic characteristics of porous metal fiber sintered sheet // Materials characterization. 2013. Vol. 86. P. 49-58.
- Ватульян А.О., Ляпин А.А. Об обратных коэффициентных задачах пороупругости // Известия Академии наук. Механика твердого тела. 2013. № 2. С. 114-121. [Vatul'yan A.O., Lyapin A.A. Ob obratnykh koeffitsientnykh zadachakh porouprugosti [On the inverse problem poroelasticity]. Izvestiya Akademii nauk. Mekhanika tverdogo tela [Proc. of the Russian Academy of Sciences. Mechanics of Solids], 2013, no. 2, pp. 114-121. (In Russian)]
- Biot M.A. Theory of Propagation of Acoustic Waves in a Fluid-Saturated Porous Solid. Part I. Low-Frequency Range // J. Acoustic. Soc. Am. 1956. Vol. 28. No. 2. P. 168-178.
Downloads
Downloads
Dates
Submitted
Accepted
Published
How to Cite
License
Copyright (c) 2015 Дударев В.В., Ляпин А.А., Святко Ю.А.
This work is licensed under a Creative Commons Attribution 4.0 International License.
