On the Motion of Shock Waves at a Constant Speed in Multimodulus Elastic Media

Dudko, O. V.; Ragozina, V. E.

doi:10.3103/s0025654418010132

Cited by 4 publications

(3 citation statements)

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“…5). In the paper [15] we describe in detail a solution including the shock wave ) ( x τ Σ with a constant velocity. This case is on the one hand a simple, and on the other hand is significant for practice.…”

Section: Nonstationary Plane 1d Motions Of An Elastic Heteromodular M...mentioning

confidence: 99%

“…2. Uniaxial compression-tension of a heteromodular half-space: (a) given boundary displacement, (b) instantaneous distribution of displacement and deformation fields at * t t t 1 > =As we shown in[15], a solution to the problem in this formulation consists of three domains I, II, III at * t t ≥ (Fig.2, b). A deformation discontinuity with the coordinate t A x H 0 = is the leading…”

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confidence: 94%

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Mathematical Modeling the Nonlinear 1D Dynamics of Elastic Heteromodular and Porous Materials

Dudko

Ragozina

Lapteva

2019

MSF

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Approaches to mathematical modeling of nonlinear strain dynamics in heteromodular and porous materials are discussed; the mechanical properties of media are described in terms of the simple piecewise linear elastic models. Several nonstationary 1D boundary value problems show that the singularity of model relationships gives rise to shock waves and centered Riemann waves in generalized solutions. Nonstationary load modes leading to the listed nonlinear effects are indicated separately for heteromodular and porous media.

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Section: Nonstationary Plane 1d Motions Of An Elastic Heteromodular M...mentioning

confidence: 99%

mentioning

confidence: 94%

Mathematical Modeling the Nonlinear 1D Dynamics of Elastic Heteromodular and Porous Materials

Dudko

Ragozina

Lapteva

2019

MSF

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“…Замена гладкой нелинейной связи на ее кусочно-линейную аппроксимацию существенно упрощает процедуру решения ряда нестационарных краевых задач одномерной динамики разномодульной среды. Так, в [31] представлены обобщенные решения с одиночными плоскими одномерными волнами деформаций, возникающими в разномодульной среде [18] при различных гладких нелинейных краевых условиях; в [32] для этой же модели получено решение одномерной задачи о гармоническом нагружении границы полупространства с чередованием ударных волн и жестких слоев; в [33][34][35] рассмотрено движение одномерных плоских и сферических волн в кусочно-линейной разномодульной среде при кусочно-гладком изменении граничной нагрузки с растяжения на сжатие или наоборот. Однако до сих пор для разномодульных материалов не затрагивался вопрос о нестационарном взаимодействии нелинейных волновых фронтов друг с другом, поскольку даже кусочно-линейные модельные соотношения не позволяют в этом случае обойтись без привлече-ния специальных приближенных методов [36].…”

Section: Introductionunclassified

Nonstationary 1D Dynamics Problems for Heteromodular Elasticity with Piecewise-Linear Approximation of Boundary Conditions

Dudko

Lapteva

Ragozina

2019

PNRPU Mechanics Bulletin

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The paper provides the investigation of a heteromodular elastic medium under dynamic loading. The heteromodularity (when the stress - strain relation depends on the deformation direction) is a distinctive feature of many natural and structural materials: rocks, porous and cohesive bulk media, fibrous and granular composites, some metal alloys, etc. The fact that the listed materials show the heteromodular property at the stage of elastic deformation should be especially taken into account when solving problems of their shock dynamics. To describe the heteromodular behavior of an elastic medium in terms of small strains we use the physically nonlinear model of V.P. Myasnikov. The accepted assumption about the one-dimensional straining reduces the nonlinear relationship of stresses and small strains to piecewise linear equations. In the case of dynamic shock deformation, the initial nonlinearity of the model is concentrated in the equations which define the velocity of the shock wave abruptly transforming the heteromodular medium from a stretched to a compressed state. In this paper we investigate the processes of generation, motion, and possible interactions of plane one-dimensional deformation waves (including shock ones) in a heteromodular elastic half-space. The points of the half-space boundary undergo one-dimensional motions according to a given non-linear law corresponding to the “stretching-compression” mode. We suggest replacing the nonstationary boundary condition of the problem by its piecewise linear approximation and constructing a connected sequence of analytical solutions with a linear boundary condition at each local time interval. The proposed approach is the basis of the numerical solving algorithm for a boundary value problem with a given nonlinear condition. It is shown that the general solution behind the shock wave consists of several local layers, which number is related to the quantity of nodes in the piecewise linear decomposition of the boundary condition. In these layers, the compression deformation is defined by the relevant part of the boundary condition and simultaneously “stores” information on the preliminary tension, which should be considered an important feature of the heteromodular medium dynamics.

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Smooth hyperelastic potentials for bimodular materials: 3D case

Kuznetsov

2024

International Journal of Non-Linear Mechanics

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On the Motion of Shock Waves at a Constant Speed in Multimodulus Elastic Media

Cited by 4 publications

References 0 publications

Mathematical Modeling the Nonlinear 1D Dynamics of Elastic Heteromodular and Porous Materials

Mathematical Modeling the Nonlinear 1D Dynamics of Elastic Heteromodular and Porous Materials

Nonstationary 1D Dynamics Problems for Heteromodular Elasticity with Piecewise-Linear Approximation of Boundary Conditions

Smooth hyperelastic potentials for bimodular materials: 3D case

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