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Javier Bonet - One of the best experts on this subject based on the ideXlab platform.

  • An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
    Computer Methods in Applied Mechanics and Engineering, 2021
    Co-Authors: Ataollah Ghavamian, Chun Hean Lee, Javier Bonet, Antonio Gil, Thomas Heuzé, Laurent Stainier
    Abstract:

    This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of Deformation measures (also known as minors of the Deformation Gradient Tensor) and the total energy of the system, extending thus the previous work carried out by some of the authors in the context of isothermal elasticity and elasto-plasticity [1-3]. To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, the internal energy density is expressed as a polyconvex combination of the triplet of Deformation measures and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where local numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. For completeness, an alternative and equally competitive formulation (in the case of smooth solutions), expressed in terms of the entropy density, is also implemented and compared. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Finite Volume Vertex Centred implementation.

  • a first order hyperbolic framework for large strain computational solid dynamics an upwind cell centred total lagrangian scheme
    International Journal for Numerical Methods in Engineering, 2017
    Co-Authors: Jibran Haider, Chun Hean Lee, Antonio J Gil, Javier Bonet
    Abstract:

    This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral Finite Volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/http://www.openfoam.com/]. In Lee, Gil and Bonet [1], a first order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the Deformation Gradient Tensor of the system, leading to excellent behaviour in two dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor-made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the Deformation Gradient Tensor must be curl-free throughout the Deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge-Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the Hyperelastic-GLACE nodal scheme of Kluth and Despr´es [2] is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications.

  • development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics
    Computers & Structures, 2013
    Co-Authors: Chun Hean Lee, Antonio J Gil, Javier Bonet
    Abstract:

    A novel computational methodology is presented for the numerical analysis of fast transient dynamics phenomena in large Deformations. The new mixed formulation can be written in the form of a system of first order conservation laws, where the linear momentum, the Deformation Gradient Tensor and the total energy of the system are used as main conservation variables, leading to identical convergence patterns for both displacements and stresses. A cell centred Finite Volume Method is utilised to carry out the spatial discretisation. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose approximate solution is derived. A suitable numerical interface flux is evaluated by means of the Rankine-Hugoniot jump conditions. We take advantage of the conservative formulation to introduce a Total Variation Diminishing shock capturing technique to improve dramatically the performance of the algorithm in the vicinity of sharp solution Gradients. A series of numerical examples will be presented in order to demonstrate the capabilities of the scheme. The new formulation is proven to be very efficient in nearly incompressible and bending dominated scenarios in comparison with classical finite element displacement-based approaches. The proposed numerical framework provides a good balance between accuracy and speed of computation.

Chun Hean Lee - One of the best experts on this subject based on the ideXlab platform.

  • An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
    Computer Methods in Applied Mechanics and Engineering, 2021
    Co-Authors: Ataollah Ghavamian, Chun Hean Lee, Javier Bonet, Antonio Gil, Thomas Heuzé, Laurent Stainier
    Abstract:

    This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of Deformation measures (also known as minors of the Deformation Gradient Tensor) and the total energy of the system, extending thus the previous work carried out by some of the authors in the context of isothermal elasticity and elasto-plasticity [1-3]. To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, the internal energy density is expressed as a polyconvex combination of the triplet of Deformation measures and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where local numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. For completeness, an alternative and equally competitive formulation (in the case of smooth solutions), expressed in terms of the entropy density, is also implemented and compared. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Finite Volume Vertex Centred implementation.

  • a first order hyperbolic framework for large strain computational solid dynamics an upwind cell centred total lagrangian scheme
    International Journal for Numerical Methods in Engineering, 2017
    Co-Authors: Jibran Haider, Chun Hean Lee, Antonio J Gil, Javier Bonet
    Abstract:

    This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral Finite Volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/http://www.openfoam.com/]. In Lee, Gil and Bonet [1], a first order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the Deformation Gradient Tensor of the system, leading to excellent behaviour in two dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor-made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the Deformation Gradient Tensor must be curl-free throughout the Deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge-Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the Hyperelastic-GLACE nodal scheme of Kluth and Despr´es [2] is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications.

  • development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics
    Computers & Structures, 2013
    Co-Authors: Chun Hean Lee, Antonio J Gil, Javier Bonet
    Abstract:

    A novel computational methodology is presented for the numerical analysis of fast transient dynamics phenomena in large Deformations. The new mixed formulation can be written in the form of a system of first order conservation laws, where the linear momentum, the Deformation Gradient Tensor and the total energy of the system are used as main conservation variables, leading to identical convergence patterns for both displacements and stresses. A cell centred Finite Volume Method is utilised to carry out the spatial discretisation. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose approximate solution is derived. A suitable numerical interface flux is evaluated by means of the Rankine-Hugoniot jump conditions. We take advantage of the conservative formulation to introduce a Total Variation Diminishing shock capturing technique to improve dramatically the performance of the algorithm in the vicinity of sharp solution Gradients. A series of numerical examples will be presented in order to demonstrate the capabilities of the scheme. The new formulation is proven to be very efficient in nearly incompressible and bending dominated scenarios in comparison with classical finite element displacement-based approaches. The proposed numerical framework provides a good balance between accuracy and speed of computation.

Laurent Stainier - One of the best experts on this subject based on the ideXlab platform.

  • An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
    Computer Methods in Applied Mechanics and Engineering, 2021
    Co-Authors: Ataollah Ghavamian, Chun Hean Lee, Javier Bonet, Antonio Gil, Thomas Heuzé, Laurent Stainier
    Abstract:

    This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of Deformation measures (also known as minors of the Deformation Gradient Tensor) and the total energy of the system, extending thus the previous work carried out by some of the authors in the context of isothermal elasticity and elasto-plasticity [1-3]. To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, the internal energy density is expressed as a polyconvex combination of the triplet of Deformation measures and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where local numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. For completeness, an alternative and equally competitive formulation (in the case of smooth solutions), expressed in terms of the entropy density, is also implemented and compared. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Finite Volume Vertex Centred implementation.

G. H. Yoon - One of the best experts on this subject based on the ideXlab platform.

  • topology optimization for stationary fluid structure interaction problems using a new monolithic formulation
    International Journal for Numerical Methods in Engineering, 2010
    Co-Authors: G. H. Yoon
    Abstract:

    This paper outlines a new procedure for topology optimization in the steady-state fluid–structure interaction (FSI) problem. A review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics (hereafter, the fluid and structural equations, respectively) and in imposing coupling boundary conditions between the separated fluid and solid domains. To overcome these difficulties, we propose an alternative monolithic procedure employing a unified domain rather than separated domains, which is not computationally efficient. In the proposed analysis procedure, the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the Deformation Gradient Tensor. For the coupling boundary conditions, the divergence of the pressure and the Darcy damping force are inserted into the solid and fluid equations, respectively. The proposed method is validated in several benchmark analysis problems. Topology optimization in the FSI problem is then made possible by interpolating Young's modulus, the fluid pressure of the modified solid equation, and the inverse permeability from the damping force with respect to the design variables. Copyright © 2009 John Wiley & Sons, Ltd.

  • topology optimization for stationary fluid structure interaction problems using a new monolithic formulation
    International Journal for Numerical Methods in Engineering, 2010
    Co-Authors: G. H. Yoon
    Abstract:

    This paper outlines a new procedure for topology optimization in the steady-state fluid-structure interaction (FSI) problem. A review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics (hereafter, the fluid and structural equations, respectively) and in imposing coupling boundary conditions between the separated fluid and solid domains. To overcome these difficulties, we propose an alternative monolithic procedure employing a unified domain rather than separated domains, which is not computationally efficient. In the proposed analysis procedure, the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the Deformation Gradient Tensor. For the coupling boundary conditions, the divergence of the pressure and the Darcy damping force are inserted into the solid and fluid equations, respectively. The proposed method is validated in several benchmark analysis problems. Topology optimization in the FSI problem is then made possible by interpolating Young's modulus, the fluid pressure of the modified solid equation, and the inverse permeability from the damping force with respect to the design variables.

Erdogan Madenci - One of the best experts on this subject based on the ideXlab platform.

  • Peridynamic correspondence model for finite elastic Deformation and rupture in Neo-Hookean materials
    International Journal of Non-Linear Mechanics, 2020
    Co-Authors: Deepak Behera, Pranesh Roy, Erdogan Madenci
    Abstract:

    Abstract This study considers finite elastic Deformation and rupture in rubber-like materials under quasi-static loading conditions by employing the bond-associated weak form of peridynamics with nonuniform horizon. The weak form of peridynamic equilibrium equation is derived based on the Neo-Hookean material model with slight compressibility. The nonlocal Deformation Gradient Tensor is computed in a bond-associated domain of interaction using the PD differential operator. This approach is free of oscillations and spurious zero energy modes that are commonly observed in the PD correspondence models. Also, it permits the direct imposition of natural and essential boundary conditions. Its fidelity for predicting large Deformation is established by comparison with those of finite element analysis of a rubber sheet with a hole under stretch. Also, its validity for predicting damage is demonstrated through simulations of experiments concerning progressive damage growth and final rupture in polymers undergoing large elastic Deformation.

  • possible causes of numerical oscillations in non ordinary state based peridynamics and a bond associated higher order stabilized model
    Computer Methods in Applied Mechanics and Engineering, 2019
    Co-Authors: Qing Zhang, Erdogan Madenci, Xiaozhou Xia
    Abstract:

    Abstract The peridynamic correspondence material model (PD CMM), generally regarded as a non-ordinary state-based peridynamic (NOSB PD) model, is attractive because of its capability to incorporate existing constitutive relations for material models. This study focuses on the mitigation of the numerical oscillations in the NOSB PD model. It compares the similarities and differences of smoothed particle hydrodynamics (SPH), corrected-SPH (CSPH), reproducing kernel particle method (RKPM), Gradient-RKPM (G-RKPM) and NOSB PD based on their Deformation Gradient Tensor and motion equations in the kernel integral form and their completeness and computational complexity. Inspired by the comparison and the peridynamic differential operator (PDDO), this study introduces a higher-order representation of the nonlocal Deformation Gradient and the force density vector by including the effect of higher-order terms in the Taylor series expansion (TSE) in order to improve the numerical accuracy and reduce the numerical oscillations. The numerical oscillations possibly arise from (1) the non-unique mapping between Deformation states and force states via converting the point-associated variables into the bond force vector in each bond within a horizon, and (2) the violation of kinematic constraint condition for each bond under an arbitrary Deformation state due to the point-associated nonlocal Deformation Gradient Tensor. Therefore, a bond-associated higher-order NOSB PD model is adopted and numerically demonstrated to be effective in improving the accuracy and completely removing the oscillations. The bond-associated force vector state eliminates the concern of non-unique mapping from a Deformation state to a force state. Also, the two bond-associated force vectors in a bond are equal and opposite, but not parallel to the bond direction. It can be viewed as a combination of the bond-based PD and the original NOSB PD. Finally, an implicit solver for both higher-order NOSB PD and bond-associated higher-order NOSB PD is presented for the solution of governing equations.

  • weak form of bond associated non ordinary state based peridynamics free of zero energy modes with uniform or non uniform discretization
    Engineering Fracture Mechanics, 2019
    Co-Authors: Erdogan Madenci, Mehmet Dorduncu, Nam Phan
    Abstract:

    Abstract The non-ordinary state-based peridynamics (NOSB PD) is attractive because of its ability to employ existing constitutive relations for material models. The Deformation Gradient Tensor and the force density vector appearing in the equilibrium equations are expressed in terms of nonlocal integrals. The definitions of these nonlocal integrals affect the accuracy and stability of PD predictions. Therefore, this study introduces a more accurate representation of the Deformation Gradient and the bond associated (BA) force density vector by using the peridynamic differential operator (PDDO). Also, it presents the weak form of BA-NOSB PD governing equations in order to impose natural and essential boundary conditions without the use of Lagrange multipliers for implicit and explicit analysis. By considering a two-dimensional rectangular plate with and without a hole under tension, the numerical results demonstrate the accuracy of BA-NOSB PD with no oscillations and zero energy modes.