A control volume procedure for solving the elastic stress-strain equations on an unstructured mesh

Fryer, Y.; Bailey, C.; Cross, M.; Lai, Chintu

doi:10.1016/s0307-904x(09)81010-x

Cited by 87 publications

(74 citation statements)

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“…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. Early attempts at applying CFD-like numerical techniques in the context of displacement based computational solid dynamics are reported in references [2,[43][44][45][46][47][48]. Eulerian Finite Volume Godunov methods, typically used for modelling compressible gas dynamics, were employed to model plastic flows in solid dynamics [49][50][51].…”

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

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%

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre

Gil

Bonet

et al. 2015

Journal of Computational Physics

152

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“…Over the last decade a number of researchers have applied FV methods to problems in CSM (see [7] for a review) and it is now possible to classify these methods into two approaches, cell-centred [8,9,10,11,12] and vertex-based [13,6,14,7].…”

Section: Introductionmentioning

confidence: 99%

“…Both classes of methods integrate governing equations over pre-defined control volumes [3,5], which are associated with the elements making up the domain of interest. Additionally, both approaches can be classified as weighted residual methods where they differ with respect to the weighting functions that are adopted [6].Over the last decade a number of researchers have applied FV methods to problems in CSM (see [7] for a review) and it is now possible to classify these methods into two approaches, cell-centred [8,9,10,11,12] and vertex-based [13,6,14,7]. …”

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confidence: 99%

“…However, if the disretisation approach is cell-centred then displacements at the boundary, for example, have to be projected from the nearest node of discretisation. Therefore, cell-centred approximations may be problematic when considering complex geometries where displacements at the boundary are not prescribed and are determined as part of the simulation.The second approach is based on traditional FE methods [2] and employs shape functions to describe the variation of an independent variable, such as displacement, over an element and is therefore well suited to complex geometries [13,6,14]. In a more general sense the approach can be classified as a Both the above FV approaches apply strict conservation over a control volume and have demonstrated superiority over traditional FE methods with regard to accuracy [10,7].…”

mentioning

confidence: 99%

“…In a more general sense the approach can be classified as a Both the above FV approaches apply strict conservation over a control volume and have demonstrated superiority over traditional FE methods with regard to accuracy [10,7]. Some researchers have attributed this to the local conservation of an independent variable as enforced by the control volumes employed [13,14] and others to the enforced continuity of the derivatives of the independent variables across cell boundaries [10]. The objectives of this paper are to describe the application of a vertex-based FV method to problems involving elasto-plastic deformation, to describe implementations and to provide a detailed comparison with a standard Galerkin FE method for an extended range of 3D elements, consisting of tetrahedral, pentahedral and hexahedral types.…”

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confidence: 99%

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A vertex‐based finite volume method applied to non‐linear material problems in computational solid mechanics

Taylor

Bailey

Cross

2002

Numerical Meth Engineering

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INTRODUCTIONOver the last three decades the FE method has firmly established itself as the standard approach for problems in computational solid mechanics (CSM), especially with regard to deformation problems involving non-linear material analysis [1,2]. As a contemporary, the FV method has similarly established itself within the field of computational fluid dynamics (CFD) [3,4]. Both classes of methods integrate governing equations over pre-defined control volumes [3,5], which are associated with the elements making up the domain of interest. Additionally, both approaches can be classified as weighted residual methods where they differ with respect to the weighting functions that are adopted [6].Over the last decade a number of researchers have applied FV methods to problems in CSM (see [7] for a review) and it is now possible to classify these methods into two approaches, cell-centred [8,9,10,11,12] and vertex-based [13,6,14,7]. The first approach is based upon traditional FV methods [3] that have been widely applied inin the context of CFD [4]. Subsequently, in the last decade such techniques have been applied to CSM problems involving structured [8,9] and unstructured meshes [15,10,11,12]. With regard to these techniques, it should be noted that when solid bodies undergo deformation the application of mechanical boundary conditions is best affected if they can be set at the physical boundary. However, if the disretisation approach is cell-centred then displacements at the boundary, for example, have to be projected from the nearest node of discretisation. Therefore, cell-centred approximations may be problematic when considering complex geometries where displacements at the boundary are not prescribed and are determined as part of the simulation.The second approach is based on traditional FE methods [2] and employs shape functions to describe the variation of an independent variable, such as displacement, over an element and is therefore well suited to complex geometries [13,6,14]. In a more general sense the approach can be classified as a Both the above FV approaches apply strict conservation over a control volume and have demonstrated superiority over traditional FE methods with regard to accuracy [10,7]. Some researchers have attributed this to the local conservation of an independent variable as enforced by the control volumes employed [13,14] and others to the enforced continuity of the derivatives of the independent variables across cell boundaries [10]. The objectives of this paper are to describe the application of a vertex-based FV method to problems involving elasto-plastic deformation, to describe implementations and to provide a detailed comparison with a standard Galerkin FE method for an extended range of 3D elements, consisting of tetrahedral, pentahedral and hexahedral types. MATHEMATICAL FORMULATIONIn this section standard mathematical models that have been employed generally in computational solid mechanics are presented. The models are described in a general sense with regard to dimension...

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A finite-volume method for deformation analysis of woven fabrics

Teng

Chen

1999

Int. J. Numer. Meth. Engng.

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SUMMARYE$cient numerical methods for simulating cloth deformations have been identi"ed as the key to the development of successful Computer-Aided Design systems for clothing products. This paper presents the formulation of a new "nite-volume method for the simulation of complex deformations of initially #at woven fabric sheets under self-weight or externally applied loading. The fabric sheet is assumed to undergo very large displacements and rotations but small strains during the process of deformation. The fabric material is assumed to be linear elastic and orthotropic. The fabric sheet is discretized into many small structured patches called "nite volumes (or control volumes), each containing one grid node and several face nodes. The bending and membrane deformations of a typical volume can be de"ned using the global co-ordinates of its grid node and surrounding face nodes. The equilibrium equations governing the complex deformations are derived employing the principle of stationary total potential energy. These equations are solved using a single-step full Newton}Raphson method which is found to be capable of predicting the "nal deformed shape, the only result of interest in a fabric drape analysis. To speed up convergence, the line search technique is adopted with good e!ect. This single-step approach is more e$cient than the step-by-step incremental approach employed in conventional non-linear "nite element analysis of load-bearing structures. A number of example simulations of fabric drape/ buckling deformations are included in the paper, which demonstrate the e$ciency and validity of the proposed method.

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A control volume procedure for solving the elastic stress-strain equations on an unstructured mesh

Cited by 87 publications

References 6 publications

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

A vertex‐based finite volume method applied to non‐linear material problems in computational solid mechanics

A finite-volume method for deformation analysis of woven fabrics

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