A Cartesian Scheme for Compressible Multimaterial Hyperelastic Models with Plasticity

Brauer, Alexia de; Iollo, Angelo; Milcent, Thomas

doi:10.4208/cicp.oa-2017-0018

Cited by 22 publications

(14 citation statements)

References 27 publications

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“…In particular, in this paper, we couple the GPR model with a simple diffuse interface approach, see [173,59,91,126]. For example, very interesting computational results with similar diffuse interface approaches and level set techniques for compressible multi-material flows have been obtained for example in [95,85,84,144,51,139,119,12]. Finally, we demonstrate that the ADER family of schemes is capable to resolve the GPR model in both solid and fluid regimes.…”

Section: Introduction and Review Of The Ader Approachmentioning

confidence: 84%

High Order ADER Schemes for Continuum Mechanics

et al. 2020

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In this paper we first review the development of high order ADER finite volume and ADER discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in 1999 by Toro et al. We show the modern variant of ADER based on a space-time predictor-corrector formulation in the context of ADER discontinuous Galerkin schemes with a posteriori subcell finite volume limiter on fixed and moving grids, as well as on space-time adaptive Cartesian AMR meshes. We then present and discuss the unified symmetric hyperbolic and thermodynamically compatible (SHTC) formulation of continuum mechanics developed by Godunov, Peshkov and Romenski (GPR model), which allows to describe fluid and solid mechanics in one single and unified first order hyperbolic system. In order to deal with free surface and moving boundary problems, a simple diffuse interface approach is employed, which is compatible with Eulerian schemes on fixed grids as well as direct Arbitrary-Lagrangian-Eulerian methods on moving meshes. We show some examples of moving boundary problems in fluid and solid mechanics.

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Section: Introduction and Review Of The Ader Approachmentioning

confidence: 84%

High Order ADER Schemes for Continuum Mechanics

et al. 2020

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“…It is interesting to note that de Brauer et al [13,10] have presented a method for multimaterial modelling of a similar system (including the distortion tensor of the GPR model, but excluding the heat conduction terms). This method is based on level sets, similar to the method presented in this paper.…”

Section: Multimaterials Modelsmentioning

confidence: 99%

A unified Eulerian framework for multimaterial continuum mechanics

Jackson

Nikiforakis

2020

Journal of Computational Physics

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A framework for simulating the interactions between multiple different continua is presented. Each constituent material is governed by the same set of equations, differing only in terms of their equations of state and strain dissipation functions. The interfaces between any combination of fluids, solids, and vacuum are handled by a new Riemann Ghost Fluid Method, which is agnostic to the type of material on either side (depending only on the desired boundary conditions).The Godunov-Peshkov-Romenski (GPR) model is used for modeling the continua (having recently been used to solve a range of problems involving Newtonian and non-Newtonian fluids, and elastic and elastoplastic solids), and this study represents a novel approach for handling multimaterial problems under this model.The resulting framework is simple, yet capable of accurately reproducing a wide range of different physical scenarios. It is demonstrated here to accurately reproduce analytical results for known Riemann problems, and to produce expected results in other cases, including some featuring heat conduction across interfaces, and impact-induced deformation and detonation of combustible materials. The framework thus has the potential to streamline development of simulation software for scenarios involving multiple materials and phases of matter, by reducing the number of different systems of equations that require solvers, and cutting down on the amount of theoretical work required to deal with the interfaces between materials.

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“…2 ), ( ) = ℱ ( )/ . В настоящее время известны и более общие виды потоков для гиперболических уравнений гиперупругости, в частности потоки типа HLLC [6,11]. В настоящей работе они не используются.…”

Section: особенности реализации схем разрывного метода галеркинаunclassified

The use of the discontinuous Galerkin method for solving one-dimensional hyperbolic problems of hyperelasticity in an inhomogeneous medium

Alekseev¹,

Савенков²

2019

KIAM Prepr.

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Применение разрывного метода Галеркина для решения одномерных гиперболических задач гиперупругости в неоднородной среде Москва, 2019 М.В. Алексеев, Е.Б. Савенков, Применение разрывного метода Галеркина для решения одномерных гиперболических задач гиперупругости в неоднородной среде Аннотация Работа посвящена численному исследованию разрывного метода Галеркина высокого порядка для решения гиперболической системы уравнений гиперупругости в неоднородной среде. Рассматриваются постановки задачи и особенности реализации вычислительных алгоритмов для системы гиперболических уравнений, записанных в консервативной и неконсервативной формах. Зоны однородности свойств среды описываются с помощью сглаженных характеристических функций. Приводятся результаты численных расчетов в однородных и неоднородных средах (газообразных и твердых) в рамках единой постановки. Ключевые слова: разрывный метод Галеркина, уравнения гиперупругости M.V. Alekseev, E.B. Savenkov The use of the discontinuous Galerkin method for solving one-dimensional hyperbolic problems of hyperelasticity in an inhomogeneous medium.

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A Cartesian Scheme for Compressible Multimaterial Hyperelastic Models with Plasticity

Cited by 22 publications

References 27 publications

High Order ADER Schemes for Continuum Mechanics

High Order ADER Schemes for Continuum Mechanics

A unified Eulerian framework for multimaterial continuum mechanics

The use of the discontinuous Galerkin method for solving one-dimensional hyperbolic problems of hyperelasticity in an inhomogeneous medium

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