Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics

Lee, Chun Hean; Gil, Antonio J.; Bonet, Javier

doi:10.1016/j.compstruc.2012.12.008

Cited by 79 publications

(232 citation statements)

References 53 publications

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“…Several authors have presented an alternative p-F mixed formulations in both Lagrangian solid and gas dynamics [1][2][3][4][40][41][42]. Specifically, in references [1,3,40,41], the authors presented a mixed conservation law for applications in Lagrangian fast solid dynamics, which are spatially discretised using tailor-made CFD technology.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, in references [1,3,40,41], the authors presented a mixed conservation law for applications in Lagrangian fast solid dynamics, which are spatially discretised using tailor-made CFD technology. The use of a mixed approach proved to be very efficient in large strain solid dynamics, circumventing the above-mentioned drawbacks for the traditional displacement based techniques.…”

Section: Introductionmentioning

confidence: 99%

“…The spatial discretisation scheme was constructed upon a Lagrangian two-field mixed (linear momentum and the deformation gradient) formulation presented as a system of conservation laws [2][3][4]. In this paper, the formulation is further enhanced by introducing a novel upwind vertex centred finite volume algorithm with three key novelties.…”

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confidence: 99%

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An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre

Gil

Bonet

et al. 2015

Journal of Computational Physics

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152

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A vertex centred Jameson-Schmidt-Turkel (JST) finite volume algorithm was recently introduced by the authors (Aguirre et al., 2014 [1]) in the context of fast solid isothermal dynamics. The spatial discretisation scheme was constructed upon a Lagrangian two-field mixed (linear momentum and the deformation gradient) formulation presented as a system of conservation laws [2][3][4]. In this paper, the formulation is further enhanced by introducing a novel upwind vertex centred finite volume algorithm with three key novelties. First, a conservation law for the volume map is incorporated into the existing two-field system to extend the range of applications towards the incompressibility limit (Gil et al., 2014 [5]). Second, the use of a linearised Riemann solver and reconstruction limiters is derived for the stabilisation of the scheme together with an efficient edge-based implementation. Third, the treatment of thermo-mechanical processes through a Mie-Grüneisen equation of state is incorporated in the proposed formulation. For completeness, the study of the eigenvalue structure of the resulting system of conservation laws is carried out to demonstrate hyperbolicity and obtain the correct time step bounds for non-isothermal processes. A series of numerical examples are presented in order to assess the robustness of the proposed methodology. The overall scheme shows excellent behaviour in shock and bending dominated nearly incompressible scenarios without spurious pressure oscillations, yielding second order of convergence for both velocities and stresses.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre

Gil

Bonet

et al. 2015

Journal of Computational Physics

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152

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“…In order to address these issues, a new mixed-formulation for Total Lagrangian fast solid dynamics has recently been proposed [4]. The new mixed-formulation consists in a system of first order conservation laws, formally akin to Computational Fluid Dynamics (CFD) models, with linear momentum and deformation gradient being the unknown conservation variables.…”

Section: Introductionmentioning

confidence: 99%

“…An explicit Total Lagrangian mixed momentum/strains formulation [1][2][3][4][5], in the form of a system of first order conservation laws, has been recently proposed to overcome the shortcomings posed by the traditional second order displacement-based formulation, namely: (1) bending and volumetric locking difficulties; (2) hydrostatic pressure fluctuations; and (3) reduced order of convergence for derived variables. Following the work of Bonet and Kulasegaram [6,7], the main objective of this paper is the adaptation of Corrected Smooth Particle Hydrodynamics (CSPH) in the context of Total Lagrangian mixed formulation.…”

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confidence: 99%

A Stabilised Total Lagrangian Corrected Smooth Particle Hydrodynamics Technique in Large Strain Explicit Fast Solid Dynamics

Greto¹,

Kulasegaram²,

Lee³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. An explicit Total Lagrangian mixed momentum/strains formulation [1][2][3][4][5], in the form of a system of first order conservation laws, has been recently proposed to overcome the shortcomings posed by the traditional second order displacement-based formulation, namely: (1) bending and volumetric locking difficulties; (2) hydrostatic pressure fluctuations; and (3) reduced order of convergence for derived variables. Following the work of Bonet and Kulasegaram [6,7], the main objective of this paper is the adaptation of Corrected Smooth Particle Hydrodynamics (CSPH) in the context of Total Lagrangian mixed formulation. Appropriate nodally conservative Jameson-Schmidt-Turkel (JST) stabilisation is introduced by taking advantage of the conservation laws. This mixed linear momentum-deformation gradient technique performs extremely well in nearly incompressible bending dominated scenarios [1, 2] without the appearance of spurious pressure oscillations. Additionally, as both linear momentum and deformation gradient are used as primary variables of the system, equal order of approximation should be achieved in both fields. A series of numerical examples are carried out to assess the applicability and robustness of the proposed algorithm.

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A 3D finite volume scheme for solving the updated Lagrangian form of hyperelasticity

Georges

Breil

Maire

2016

Numerical Methods in Fluids

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Summary The finite volume discretization of nonlinear elasticity equations seems to be a promising alternative to the traditional finite element discretization as mentioned by Lee et al. [Computers and Structures (2013)]. In this work, we propose to solve the elastic response of a solid material by using a cell‐centered finite volume Lagrangian scheme in the current configuration. The hyperelastic approach is chosen for representing elastic isotropic materials. In this way, the constitutive law is based on the principle of frame indifference and thermodynamic consistency, which are imposed by mean of the Coleman–Noll procedure. It results in defining the Cauchy stress tensor as the derivative of the free energy with respect to the left Cauchy–Green tensor. Moreover, the materials being isotropic, the free‐energy is function of the left Cauchy–Green tensor invariants, which enable the use of the neo‐Hookean model. The hyperelasticity system is discretized using the cell‐centered Lagrangian scheme from the work of Maire et al. [J. Comput. Phys. (2009)]. The 3D scheme is first order in space and time and is assessed against three test cases with both infinitesimal displacements and large deformations to show the good accordance between the numerical solutions and the analytic ones. Copyright © 2016 John Wiley & Sons, Ltd.

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Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics

Cited by 79 publications

References 53 publications

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

A Stabilised Total Lagrangian Corrected Smooth Particle Hydrodynamics Technique in Large Strain Explicit Fast Solid Dynamics

A 3D finite volume scheme for solving the updated Lagrangian form of hyperelasticity

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