Development of a stabilised Petrov–Galerkin formulation for conservation laws in Lagrangian fast solid dynamics

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

doi:10.1016/j.cma.2013.09.004

Cited by 59 publications

(191 citation statements)

References 83 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%

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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%

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre

Gil

Bonet

et al. 2015

Journal of Computational Physics

Self Cite

152

View full text Add to dashboard Cite

show abstract

“…Adding JST has the dual aim of (a) accurately representing potential discontinuities in the solution, and (b) introducing artificial dissipation to it where continuous. In [3], stabilisation is achieved through the use of Petrov-Galerkin algorithm. All these attempts have yielded promising results in two-and threedimensional applications, with velocities (or displacements) and stresses (or strains) achieving the same degree of accuracy.…”

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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“…All these mixed schemes are stabilized via the Variational Multi-Scale method (VMS) [21,31,32,33,41], and, specifically, the Orthogonal Subgrid Scales method, in order to gain control of all the variables while circumventing the restrictiveness of the inf-sup compatibility conditions on the choice of the interpolation spaces. Similar mixed approaches have been proposed using alternative stabilization techniques, like SUPG [4,5,29,36] or FIC [41].…”

Section: Introductionmentioning

confidence: 99%

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

et al. 2016

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K: explicit mixed finite elements, stabilization, incompressibility, plasticity, strain softening, strain localization, mesh independence. AbstractThis paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P 1P 1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.

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Development of a stabilised Petrov–Galerkin formulation for conservation laws in Lagrangian fast solid dynamics

Cited by 59 publications

References 83 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

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

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