Mathematical Aspects of Numerical Solution of Hyperbolic Systems

Куликовский, А. Г.; Pogorelov, N. V.; Semenov, A. Yu.

doi:10.1201/9781482273991

Cited by 217 publications

(156 citation statements)

References 7 publications

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“…This type of model is commonly used at engineering level and is implemented in many numerical codes such as OURANOS of the Direction Générale de l'Armement and the Commissariat à l'Energie Atomic (France) or a shock wave physics computer code (called CTH) developed at the Sandia National Laboratory (USA). For such models, the Maxwell relaxation equation for the deviatoric part of the stress tensor is used [1,2]. Compatibility of these models with the objectivity principle and with general thermodynamical principles is not straightforward.…”

Section: Introductionmentioning

confidence: 99%

Mathematical and numerical model for nonlinear viscoplasticity

Favrie

Gavrilyuk

2011

Phil. Trans. R. Soc. A.

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A macroscopic model describing elastic-plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In addition, Maxwell-type material behaviour is shown up: the deviatoric part of the stress tensor decays during plastic deformations. Numerical examples show the ability of this model to deal with real physical phenomena.

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Section: Introductionmentioning

confidence: 99%

Mathematical and numerical model for nonlinear viscoplasticity

Favrie

Gavrilyuk

2011

Phil. Trans. R. Soc. A.

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“…The plastic stage is described by a system which is obtained from (8) by replacing the last equation on the equation (10). From this system one can find…”

Section: Radial Expansion Of Cavitiesmentioning

confidence: 99%

“…For the solution of 1D systems of equations an explicit monotone finite-difference ENO-scheme of the "predictor-corrector" type with piecewise-linear distributions of velocities and stresses over meshes, based on the principles of grid-characteristic methods [10], is applied. The parallelizing of computations is carried out using the MPI library, the programming language is Fortran.…”

Section: Computational Algorithmmentioning

confidence: 99%

Phenomenological Modeling of Deformation of Porous and Cellular Materials Taking Into Account the Increase in Stiffness Because of the Collapse of Pores

Sadovskii¹,

Sadovskaya²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. Mathematical model for the description of deformation of a porous material with a random distribution of pores is constructed on the basis of generalized rheological method taking into account the different resistance of a material to tension and compression. Phenomenological parameters of the model are determined by means of the approximate computations for the problem of static loading of a cubic periodicity cell with spherical cavities. Within the framework of this theory the fields of displacements and stresses around expanding cavity of spherical shape in a homogenious space are constructed. It is shown that the porosity does not change at the stage of elastic deformation. When the pressure increases, a zone of plastic compaction is formed in the vicinity of a cavity, and in a part of this zone the collapse of pores takes place. Engineering formulas for calculation of critical pressures of the elastic limit state and the limit state of a medium with open pores, and also the formulas for determining the radiuses of interfaces of zones of plasticity and compaction are obtained. A complex of parallel programs for numerical analysis of the dynamic deformation of porous materials on multiprocessor computer systems is worked out. By means of this complex a series of computations for deformation of the protection elements, made of metal foams, under the action of localized impulsive loads was performed. The random nature of distribution of the pores size is taken into account with the help of computer modeling. Computations allow one to estimate plastic dissipative part of the energy of impact.

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“…На основе этих решений С.К. Годуновым был развит численный ме-тод [11,12] расчета гиперболических систем уравнений [13]. Несмотря на то, что метод известен уже давно, его положительные качества, такие как явное определение вида исходящих разрывов, в том числе и на неструктурированных сетках [14], привлекают к нему внимание, и метод продолжает активно со-вершенствоваться [15,16].…”

Section: Introductionunclassified

Arbitrary interaction of plane supersonic flows

Булат¹,

Волков²

2015

Naučno-teh. vestn. inf. tehnol. meh. opt.

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Mathematical Aspects of Numerical Solution of Hyperbolic Systems

Cited by 217 publications

References 7 publications

Mathematical and numerical model for nonlinear viscoplasticity

Mathematical and numerical model for nonlinear viscoplasticity

Phenomenological Modeling of Deformation of Porous and Cellular Materials Taking Into Account the Increase in Stiffness Because of the Collapse of Pores

Arbitrary interaction of plane supersonic flows

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