An exact Riemann solver for one‐dimensional multimaterial elastic‐plastic flows with Mie‐Grüneisen equation of state without vacuum

Liu, Li; Cheng, Jianwei; Shen, Yongxing

doi:10.1002/fld.4917

Cited by 4 publications

(3 citation statements)

References 42 publications

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“…In the governing equations, two separate transport equations for elas-tic and plastic deformation tensors are combined with other conservation laws. Liu et al [23] modeled one-dimensional multi-material elastic-plastic flow using a Riemann solver. By using finite volume method with stationary grids in Eulerian frame, conservation laws and modified hypoelastic Wilkins model were solved to find the cause of adiabatic shear bands formation [24].…”

Section: Introductionmentioning

confidence: 99%

Simulation of Wave in Hypo-Elastic-Plastic Solids Modeled by Eulerian Conservation Laws

Yang¹,

Lowe²

2023

Preprint

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This paper reports a theoretical and numerical framework to model nonlinear waves in elastic-plastic solids. Formulated in the Eulerian frame, the governing equations employed include the continuity equation, the momentum equation, and an elastic-plastic constitutive relation. The complete governing equations are a set of first-order, fully coupled partial differential equations with source terms. The primary unknowns are velocities and deviatoric stresses. By casting the governing equations into a vector-matrix form, we derive the eigenvalues of the Jacobian matrix to show the wave speeds. The eigenvalues are also used to calculate the Courant number for numerical stability. The model equations are solved using the Space-Time Conservation Element and Solution Element (CESE) method. The approach is validated by comparing our numerical results to an analytical solution for the special case of longitudinal wave motion.

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Section: Introductionmentioning

confidence: 99%

Simulation of Wave in Hypo-Elastic-Plastic Solids Modeled by Eulerian Conservation Laws

Yang¹,

Lowe²

2023

Preprint

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“…Exact Riemann solvers for convex dynamics have been proposed for different scenarios (Declercq et al. 2000; Giacomazzo & Rezzolla 2006; Zhiqiang 2010; Huahui & Zhiqiang 2016; Zhiqiang 2018; Liu, Cheng & Shen 2021; Minatti & Faggioli 2023). More complex scenarios have been studied for general systems of conservation laws (Liu 1975) and treated in non-convex Newtonian dynamics (Muller & Voss 2006).…”

Section: Introductionmentioning

confidence: 99%

“…The exact solution of the Riemann problem in SRHD has been studied for the case of convex dynamics, where only simple nonlinear waves are developed (Martí & Müller 1994;Pons, Martí & Müller 2000;Rezzolla & Zanotti 2001;Rezzolla, Zanotti & Pons 2003). Exact Riemann solvers for convex dynamics have been proposed for different scenarios (Declercq et al 2000;Giacomazzo & Rezzolla 2006;Zhiqiang 2010;Huahui & Zhiqiang 2016;Zhiqiang 2018;Liu, Cheng & Shen 2021;Minatti & Faggioli 2023). More complex scenarios have been studied for general systems of conservation laws (Liu 1975) and treated in non-convex Newtonian dynamics (Muller & Voss 2006).…”

Section: Introductionmentioning

confidence: 99%

Exact Riemann solver for non-convex relativistic hydrodynamics

Berbel,

Serna,

Marquina

2023

J. Fluid Mech.

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We present the general analytical solution of the Riemann problem (decay of a jump discontinuity) for non-convex relativistic hydrodynamics. In convex dynamics, an elementary nonlinear wave, i.e. a rarefaction or a shock, originates at the discontinuity and travels towards one of the initial states. Between the left and right waves, an equilibrium state appears represented by a contact discontinuity. The exact solution to the Riemann problem in convex relativistic hydrodynamics was first addressed by Martí & Müller (J. Fluid Mech., vol. 258, 1994, pp. 317–333). In non-convex dynamics, two sequences of elementary nonlinear waves move towards the left and right initial states. Solving the Riemann problem involves determining the types of wave developing and the equilibrium state where they coincide. The procedure consists of constructing the wave curves associated with the nonlinear waves in the pressure–velocity phase space, where the intersection of the wave curves indicates the equilibrium state. We describe the relation between the wave curves, the explicit formulas for their calculation, and the outline of the process for a correct derivation and representation of the waves in the spatial domain. We present examples of the exact solution of a Riemann problem that illustrate the complex phenomena of non-convex dynamics by using the phenomenological non-convex equation of state proposed by Ibáñez et al. (Mon. Not. R. Astron. Soc., vol. 476, 2017, pp. 1100–1110).

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An entropy-stable updated reference Lagrangian smoothed particle hydrodynamics algorithm for thermo-elasticity and thermo-visco-plasticity

et al. 2023

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This paper introduces a novel upwind Updated Reference Lagrangian Smoothed Particle Hydrodynamics (SPH) algorithm for the numerical simulation of large strain thermo-elasticity and thermo-visco-plasticity. The deformation process is described via a system of first-order hyperbolic conservation laws expressed in referential description, chosen to be an intermediate configuration of the deformation. The linear momentum, the three incremental geometric strains measures (between referential and spatial domains), and the entropy density of the system are treated as conservation variables of this mixed coupled approach, thus extending the previous work of the authors in the context of isothermal elasticity and elasto-plasticity. To guarantee stability from the SPH discretisation standpoint, appropriate entropy-stable upwinding stabilisation is suitably designed and presented. This is demonstrated via the use of the Ballistic free energy of the coupled system (also known as Lyapunov function), to ensure the satisfaction of numerical entropy production. An extensive set of numerical examples is examined in order to assess the applicability and performance of the algorithm. It is shown that the overall algorithm eliminates the appearance of spurious modes (such as hour-glassing and non-physical pressure fluctuations) in the solution, typical limitations observed in the classical Updated Lagrangian SPH framework.

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An exact Riemann solver for one‐dimensional multimaterial elastic‐plastic flows with Mie‐Grüneisen equation of state without vacuum

Cited by 4 publications

References 42 publications

Simulation of Wave in Hypo-Elastic-Plastic Solids Modeled by Eulerian Conservation Laws

Simulation of Wave in Hypo-Elastic-Plastic Solids Modeled by Eulerian Conservation Laws

Exact Riemann solver for non-convex relativistic hydrodynamics

An entropy-stable updated reference Lagrangian smoothed particle hydrodynamics algorithm for thermo-elasticity and thermo-visco-plasticity

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