An upwind vertex centred finite volume algorithm for nearly and truly incompressible explicit fast solid dynamic applications: Total and Updated Lagrangian formulations

Hassan, Osama I.; Ghavamian, Ataollah; Lee, Chun Hean; Gil, Antonio J.; Bonet, Javier; Auricchio, Ferdinando

doi:10.1016/j.jcpx.2019.100025

Cited by 12 publications

(40 citation statements)

References 66 publications

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“…Definition of these terms follows via the semi-discrete version of the Colemann-Noll procedure [94] in order to ensure the production of numerical entropy. This will be discussed in the following section.…”

Section: Total Lagrangian Sph Discrete Formulationmentioning

confidence: 99%

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

et al. 2021

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This paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure.

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Section: Total Lagrangian Sph Discrete Formulationmentioning

confidence: 99%

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

et al. 2021

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“…In recent years, the research group at Swansea University have pursued the same {p, F } system whilst exploiting a wide range of spatial discretisation techniques including upwind cell centred FVM [6,18], Jameson-Schmidt-Turkel vertex centred FVM [118], upwind VCFVM [7,16], two step Taylor-Galerkin FEM [119] and stabilised Petrov-Galerkin FEM [17]. In subsequent papers, the {p, F } system was then augmented by incorporating a new conservation law for the Jacobian of the deformation J [7,16,23] to effectively solve nearly incompressible deformations. Moreover, the {p, F , J} formulation was also extended to account for truly incompressible materials utilising a tailor-made fractional step approach [16,120].…”

Section: Mixed-based Methodologymentioning

confidence: 99%

“…In subsequent papers, the {p, F } system was then augmented by incorporating a new conservation law for the Jacobian of the deformation J [7,16,23] to effectively solve nearly incompressible deformations. Moreover, the {p, F , J} formulation was also extended to account for truly incompressible materials utilising a tailor-made fractional step approach [16,120]. Further enhancement of this framework has recently been reported [3,120], when considering materials governed by a polyconvex constitutive law where the co-factor H of the deformation plays a dominant role.…”

Section: Mixed-based Methodologymentioning

confidence: 99%

“…In general, to perform a numerical modelling in the context of solid dynamics, one might use the existing commercial packages (ANSYS AUTODYN, LS-DYNA and ABAQUS to name a few), open source software (Codeaster, FEM-based; OpenFOAM, FVM-based; and Dual-SPHysics, SPH-based) or in-house computer software. By using commercial software, it is possible to numerically simulate a wide range of applications, such as fracture and fragmentation, metal forming and additive manufacturing processes, contact and hypervelocity impact [16]. These numerical tools are typically developed on the basis of classical low order finite element displacement-based formulations and, consequently, suffer from a certain number of numerical difficulties (locking, hour-glass modes and spurious pressure oscillations) [7,17,18].…”

Section: List Of Tablesmentioning

confidence: 99%

“…These numerical tools are typically developed on the basis of classical low order finite element displacement-based formulations and, consequently, suffer from a certain number of numerical difficulties (locking, hour-glass modes and spurious pressure oscillations) [7,17,18]. Although some modifications have been applied to commercial tools to alleviate some of these shortcomings [14,[19][20][21], numerical difficulties are still evident when dealing with nearly/truly incompressible materials [16,22]. Additionally, the shock-capturing technologies are poorly developed in the context of solid dynamics [6,7,18,23].…”

Section: List Of Tablesmentioning

confidence: 99%

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A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity

Ghavamian

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It is evidently not trivial to analytically solve practical engineering problems due to their inherent (geometrical and/or material) nonlinearities. Moreover, experimental testing can be extremely costly, time-consuming and even dangerous, in some cases. In the past few decades, therefore, numerical techniques have been progressively developed and utilised in order to investigate complex engineering applications through computer simulations, in a cost-eﬀective manner.An important feature of a numerical methodology is how to approximate a physical domain into a computational domain and that, typically, can be carried out via mesh-based and particle-based approximations, either of which manifest with a diﬀerent range of capabilities. Due to the geometrical complexity of many industrial applications (e.g. biomechanics, shape casting, metal forming, additive manufactur-ing, crash simulations), a growing attraction has been received by tetrahedral mesh generation, thanks to Delaunay and advancing front techniques [1, 2]. Alternatively, particle-based methods can be used as they oﬀer the possibility of tackling speciﬁc applications in which mesh-based techniques may not be eﬃcient (e.g. hyper velocity impact, astrophysics, failure simulations, blast).In the context of fast thermo-elastodynamics, modern commercial packages are typically developed on the basis of second order displacement-based ﬁnite element formulations and, unfortunately, that introduces a series of numerical shortcomings such as reduced order of convergence for strains and stresses in comparison with displacements and the possible onset of numerical instabilities (e.g. detrimental locking, hour-glass modes, spurious pressure oscillations).To rectify these drawbacks, a mixed-based set of ﬁrst order hyperbolic conservation laws for isothermal elastodynamics was presented in [3–6], in terms of the linear momentum p per unit undeformed volume and the minors of the deformation, namely, the deformation gradient F , its co-factor H and its Jacobian J. Taking inspiration of these works [4, 7] and in order to account for irreversible processes, the balance of total energy (also known as the ﬁrst law of thermodynamics) is incorporated to the set of physical laws used to describe the deformation process. This, in general, can be expressed in terms of the entropy density η or total energy density E by which the Total Lagrangian entropy-based and total energy-based formulations {p, F , H, J, η or E} are established, respectively. Interestingly, taking advantage of the conservation formulation framework, it is possible to bridge the gap between solid dynamics and Computational Fluid Dynamics (CFD) by exploiting available CFD techniques in the context of solid dynamics.From a computational standpoint, two distinct and extremely competitive spatial discretisations are employed, namely, mesh-based Vertex-Centred Finite Volume Method (VCFVM) and meshless Smooth Particle Hydrodynamics (SPH). A linear reconstruction procedure together with a slope limiter is employed in order to ensure second order accuracy in space whilst avoiding numerical oscillations in the vicinity of sharp gradients, respectively. Crucially, the discontinuous solution for the conservation variables across (dual) control volume interfaces or between any pair of particles is approximated via an acoustic Riemann solver. In addition, a tailor-made artiﬁcial compressibility algorithm and an angular momentum preservation scheme are also incorporated in order to assess same limiting scenarios.The semi-discrete system of equations is then temporally discretised using a one-step two-stage Total Variation Diminishing (TVD) Runge-Kutta time integrator, providing second order accuracy in time. The geometry is also monolithically updated to be only used for post-processing purposes.Finally, a wide spectrum of challenging examples is presented in order to assess both the performance and applicability of the proposed schemes. The new formulation is proven to be very eﬃcient in nearly incompressible thermo-elasticity in comparison with classical ﬁnite element displacement-based approaches. The proposed computational framework provides a good balance between accuracy and speed of computation.

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An acoustic Riemann solver for large strain computational contact dynamics

Runcie

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Haider³

et al. 2022

Numerical Meth Engineering

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This article presents a vertex-centered finite volume algorithm for the explicit dynamic analysis of large strain contact problems. The methodology exploits the use of a system of first order conservation equations written in terms of the linear momentum and a triplet of geometric deformation measures (comprising the deformation gradient tensor, its co-factor, and its Jacobian) together with their associated jump conditions. The latter can be used to derive several dynamicconservation laws, explicit contact dynamics, large strain, OpenFOAM, Riemann solver, shocksThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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An upwind vertex centred finite volume algorithm for nearly and truly incompressible explicit fast solid dynamic applications: Total and Updated Lagrangian formulations

Cited by 12 publications

References 66 publications

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity

An acoustic Riemann solver for large strain computational contact dynamics

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