[Text] / O. V. Sadovskaya, V. M. Sadovskii, M. P. Varygina // ECCOMAS Thematic Conference - COMPDYN 2013: 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Proceedings - An IACM Special Interest Conference. - 2013. - P4578-4592
Аннотация: In the framework of mathematical model of a block medium with elastic blocks interacting through compliant viscoelastic interlayers and its approximation on the basis of equations of the Cosserat continuum, the problems of periodic perturbation of a layer and of a half-space under the action of distributed and localized surface loads are solved numerically. The simple formulas are suggested to determine the elasticity coefficients of the moment continuum by given characteristics of the materials of blocks and interlayers, which provide a good correspondence of the wave fields received by means of the exact and approximate models. Parallel computational algorithms, based on models of the inhomogeneous elasticity theory and the Cosserat elasticity theory, are applied to the analysis of propagation of elastic waves in geomaterials with layered and block microstructure. These algorithms are realized as parallel program systems for GPUs (using CUDA technology) and for multiprocessor computers of the cluster type (using MPI library). Monotone grid-characteristic schemes with a balanced number of time steps in elastic layers or blocks and in viscoelastic interlayers are used. By the analysis of numerical solutions it is shown that the multiblock medium has a resonant frequency of rotational motion of blocks, and this frequency does not depend on the size of a massif and on the boundary conditions at its surface.
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Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович; Varygina, M.P.; Варыгина, Мария Петровна; Садовская, Оксана Викторовна
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Computational modeling of the waves propagation in a block medium with viscoelastic interlayers
Mathematical and numerical modelling of porous geomaterials based on generalized rheological approach
/ V. M. Sadovskii, O. V. Sadovskaya // 9th Australasian Congress on Applied Mechanics, ACAM 2017 : National Committee on Applied Mechanics, 2017. - Vol. 2017-November: 9th Australasian Congress on Applied Mechanics, ACAM 2017 (27 November 2017 through 29 November 2017, ) Conference code: 135086
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Кл.слова (ненормированные):
Elasticity -- Granular medium -- Parallel algorithm -- Plasticity -- Porous geomaterial -- Rheology -- Elasticity -- Geometry -- Interface states -- Parallel algorithms -- Plasticity -- Porous materials -- Rheology -- Shock waves -- Supercomputers -- Characteristic zones -- Computational algorithm -- Elastic longitudinal waves -- Geomaterials -- Granular medium -- Instantaneous loading -- Longitudinal compression -- Tension and compression -- Compaction
Аннотация: Traditional rheological method is supplemented by a new element called rigid contact, which serves to take into account different resistance of materials to tension and compression. Based on this method, mathematical model describing deformation of a porous medium is constructed, which takes into account change in the resistance to external mechanical impact at a moment of collapse of pores. Parallel computational algorithm is developed for the analysis of dynamics of porous materials, accompanied by plastic deformation of skeleton and collapse of pores. This algorithm is tested on supercomputers in the problems about propagation of plane longitudinal compression shock waves and the expansion of cylindrical cavity in an infinite porous medium. The solutions of these problems are obtained in closed form in the framework of the suggested mathematical model. It is shown that, depending on the porosity of the medium and the value of the yield point, the instantaneous loading of a half-space with constant pressure leads to the formation of one or two shock waves – an elastic longitudinal wave, a plastic wave or waves of elastic or plastic compaction. Critical pressures of limit states and radii of interfaces between characteristic zones of plasticity and compaction are calculated numerically in the problem of radial expansion of cavity with sufficiently high precision. © 2017 National Committee on Applied Mechanics. All Rights Reserved.
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Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok 50/44, Krasnoyarsk, 660036, Russian Federation
Доп.точки доступа:
Sadovskii, V. M.; Sadovskaya, O. V.
Кл.слова (ненормированные):
Elasticity -- Granular medium -- Parallel algorithm -- Plasticity -- Porous geomaterial -- Rheology -- Elasticity -- Geometry -- Interface states -- Parallel algorithms -- Plasticity -- Porous materials -- Rheology -- Shock waves -- Supercomputers -- Characteristic zones -- Computational algorithm -- Elastic longitudinal waves -- Geomaterials -- Granular medium -- Instantaneous loading -- Longitudinal compression -- Tension and compression -- Compaction
Аннотация: Traditional rheological method is supplemented by a new element called rigid contact, which serves to take into account different resistance of materials to tension and compression. Based on this method, mathematical model describing deformation of a porous medium is constructed, which takes into account change in the resistance to external mechanical impact at a moment of collapse of pores. Parallel computational algorithm is developed for the analysis of dynamics of porous materials, accompanied by plastic deformation of skeleton and collapse of pores. This algorithm is tested on supercomputers in the problems about propagation of plane longitudinal compression shock waves and the expansion of cylindrical cavity in an infinite porous medium. The solutions of these problems are obtained in closed form in the framework of the suggested mathematical model. It is shown that, depending on the porosity of the medium and the value of the yield point, the instantaneous loading of a half-space with constant pressure leads to the formation of one or two shock waves – an elastic longitudinal wave, a plastic wave or waves of elastic or plastic compaction. Critical pressures of limit states and radii of interfaces between characteristic zones of plasticity and compaction are calculated numerically in the problem of radial expansion of cavity with sufficiently high precision. © 2017 National Committee on Applied Mechanics. All Rights Reserved.
Scopus
Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok 50/44, Krasnoyarsk, 660036, Russian Federation
Доп.точки доступа:
Sadovskii, V. M.; Sadovskaya, O. V.