Solid–fluid diffuse interface model in cases of extreme deformations

Favrie, Nicolas; Gavrilyuk, Sergey; Saurel, Richard

doi:10.1016/j.jcp.2009.05.015

Cited by 129 publications

(138 citation statements)

References 36 publications

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“…For large solicitations, we recover the fluid behaviour (2.3). The choice (2.3) and (2.4) guarantees, in particular, the hyperbolicity of equations (2.1) in the one-dimensional case [16], and hence the well-posedness of the corresponding Cauchy problem. The stress tensor will then be s = −2r ve vĜĜ = −pI + S…”

Section: Governing Equations Of Isotropic Elastic Solidsmentioning

confidence: 99%

“…Under some natural constraints, this choice guarantees the hyperbolicity of the governing equations in the whole domain of parameters (e.g. [16]). We use the relaxation system for the eigenvalues of G, and show that the resulting equations are compatible, not only with the mass conservation law, but also the entropy inequality and the von Mises yield condition.…”

Section: The Solution Of These Equations Ismentioning

confidence: 99%

“…Let us consider an impact of a solid copper projectile on a solid copper plate (figure 4). Such a problem has already been studied in an elastic case in Favrie et al [16]. The copper projectile has an initial velocity u = 500 m s A small amount of air (a g = 10 −4 ) is present in the solid.…”

Section: Diffuse Interface Modelmentioning

confidence: 99%

See 2 more Smart Citations

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: Governing Equations Of Isotropic Elastic Solidsmentioning

confidence: 99%

Section: The Solution Of These Equations Ismentioning

confidence: 99%

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Mathematical and numerical model for nonlinear viscoplasticity

Favrie

Gavrilyuk

2011

Phil. Trans. R. Soc. A.

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“…We have seen that two tensors (any two among the three tensors F , E, P ) are needed to compute stresses in the Lagrangian framework (see (36)). The situation is different in the Eulerian framework.…”

Section: Strainsmentioning

confidence: 99%

Irreversible mechanics and thermodynamics of two-phase continua experiencing stress-induced solid–fluid transitions

Peshkov

Grmela

Romenski

2014

Continuum Mech. Thermodyn.

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On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the time evolution equations possessing it are compatible with mechanics and with thermodynamics. The former compatibility means that the equations are local conservation laws of the Godunov type and the latter compatibility means that the entropy does not decrease during the time evolution. In numerical illustrations, in which the one-dimensional Riemann problem is explored, we require that the Euler structure is also preserved in the discretization.

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“…Material interface problems [15], chemical reactions [16], phase change [17], surface tension [18], solid-fluid [19], plastic transformation [20], dense and dilute flows [21], and shallow water flows [22] can be cited for instance. In these flow models, compressibility of each phase is responsible for the hyperbolic character of the equations and an appropriate and convex EOS is required for each fluid.…”

Section: Introductionmentioning

confidence: 99%

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Chiapolino

Saurel

2018

Fluids

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Abstract:The Noble-Abel Stiffened-Gas (NASG) equation of state (Le Métayer, O. and Saurel, R. proposed in 2016) is extended to variable attractive and repulsive effects to improve the liquid phase accuracy when large temperature and pressure variation ranges are under consideration. The transition from pure phase to supercritical state is of interest as well. The gas phase is considered through the ideal gas assumption with variable specific heat rendering the formulation valid for high temperatures. The liquid equation-of-state constants are determined through the saturation curves making the formulation suitable for two-phase mixtures at thermodynamic equilibrium. The overall formulation is compared to experimental characteristic curves of the phase diagram showing good agreement for various fluids (water, oxygen). Compared to existing cubic equations of state, the present one is convex, a key feature for computations with hyperbolic flow models.

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Solid–fluid diffuse interface model in cases of extreme deformations

Cited by 129 publications

References 36 publications

Mathematical and numerical model for nonlinear viscoplasticity

Mathematical and numerical model for nonlinear viscoplasticity

Irreversible mechanics and thermodynamics of two-phase continua experiencing stress-induced solid–fluid transitions

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

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