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An Energy-Based Variational Model of Ferromagnetic Hysteresis for Finite Element Computations François-Lavet, Vincent ; ; Stainier, Laurent et al in Journal of Computational & Applied Mathematics (2013), 246 This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic ... [more ▼] This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. [less ▲] Detailed reference viewed: 268 (48 ULg)A two-scale model predicting the mechanical sliding and opening behavior of grain boundaries in nanocrystalline solids Péron-Lührs, Vincent ; ; et al in Hogge, Michel; Van Keer, Roger; Dick, Erik (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November) In polycrystalline materials with nanosized grains smaller than 100 nm, the deformation mechanisms taking place at grain boundaries (GBs) become dominant compared to intragranular crystal plasticity ... [more ▼] In polycrystalline materials with nanosized grains smaller than 100 nm, the deformation mechanisms taking place at grain boundaries (GBs) become dominant compared to intragranular crystal plasticity. Recent studies have revealed that more accurate mechanical properties can be obtained by choosing the relevant GB character distribution (GBCD). We use here a numerical multiscale approach (an extension of a previous work [1]) to predict the mechanical behavior of nanostructured metals according to their GBCD composed of either high angle GBs (HAB) or low angle GBs (LAB). The quasicontinuum method (QC) is used to obtain the GB mechanical response at the nanoscale under simple shear (sliding part) and tensile load (opening part). These QC results are then used in a finite element code (direct numerical simulation-DNS) as GB constitutive models. This two-scale framework does not suffer from length scales limitations conventionally encountered when considering the two scales separately. [less ▲] Detailed reference viewed: 124 (30 ULg)Vectorial Incremental Nonconservative Consistent Hysteresis model François-Lavet, Vincent ; ; Stainier, Laurent et al in Hogge, Michel; Van Keer, Roger; Malengier, Benny (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November) This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic ... [more ▼] This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. [less ▲] Detailed reference viewed: 97 (14 ULg)Actes du Congrès ACOMEN 2008, Second international Conference on Advanced Computational Methods in Engineering, Liège, Belgium, May 26-38, 2008. Hogge, Michel ; ; Noels, Ludovic et al Book (2008) Detailed reference viewed: 63 (6 ULg)A first-order energy-dissipative momentum-conserving scheme for elasto-plasticity using the variational updates formulation Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in Computer Methods in Applied Mechanics & Engineering (2008), 197(6-8), 706726 In a previous paper [L. Noels, L. Stainier, J.-P. Ponthot, An energy momentum conserving algorithm using the variational formulation of visco-plastic updates, Int. J. Numer. Methods Engrg. 65 (2006) 904 ... [more ▼] In a previous paper [L. Noels, L. Stainier, J.-P. Ponthot, An energy momentum conserving algorithm using the variational formulation of visco-plastic updates, Int. J. Numer. Methods Engrg. 65 (2006) 904-942] the authors demonstrated the efficiency of the variational formulation of elasto-plastic updates to develop energy-momentum conserving time integration algorithms. Indeed, within such a framework, the stress tensor always derives from an incremental potential, even when plastic behavior is considered. Therefore the verification of the conservation of energy in the non-linear range can easily be demonstrated: the sum of the reversible stored energy and irreversible dissipated energy exactly corresponds to the work of the external forces applied to the structure. Although this formulation was shown to be accurate and robust, the introduction of numerical dissipation for high-frequency numerical modes can be necessary to simulate complex phenomena. In this work, we propose a modification of the variational updates framework to introduce this numerical property, leading to a new energy-dissipative momentum-conserving time-integration algorithm for elasto-plasticity. (c) 2007 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 66 (18 ULg)A comparison of triangle and quadrangle finite elements for large strain elastoplastic formulations ; Stainier, Laurent ; et al in Proceedings of ACOMEN’2008, Advanced Computational Methods in Engineering (2008) The paper presents a comparative study of different elastoplastic large strain formulations used in research groups in Mendoza and Li`ege. The comparison is focused on a few academic standardized problems ... [more ▼] The paper presents a comparative study of different elastoplastic large strain formulations used in research groups in Mendoza and Li`ege. The comparison is focused on a few academic standardized problems, in particular necking of a cylindrical bar in tension. Stress distribution at necking section, as well as load histories are analyzed for all three formulations. Two other test cases consider bending of the so-called ”Greco” beam and upsetting of a cylinder. Numerical results show that all approaches yield very similar results and thus are equally valid. Furthermore, quadratic 6-noded triangles provide a good alternative to bilinear quadrangles, even if sometimes they appear to be more sensitive to big distorsions. [less ▲] Detailed reference viewed: 111 (6 ULg)Identificación de parámetros de viscoelasticidad finita aplicada a la simulación del comportamiento mecánico de masa encefálica ; ; Noels, Ludovic et al in Congreso Iberoamericano de Ingenieria Mecanica (2007, October) Detailed reference viewed: 350 (11 ULg)Introduction of Numerical Dissipation in the Variational Updates Framework for Elasto-Plastic Constitutive Models Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe (2007) The most widely used time integration algorithms for finite-element, based on the Newmark family, are numerically stable only for linear models. Using a variational formulation of elasto-plastic updates ... [more ▼] The most widely used time integration algorithms for finite-element, based on the Newmark family, are numerically stable only for linear models. Using a variational formulation of elasto-plastic updates for which the stress tensor always derives from an incremental potential, even when plastic behavior is considered, a new Energy-Dissipative Momentum Conserving time integration algorithms can easily be developed. Indeed, the incremental potential guarantees the verification of the numerical dissipation of energy for non-linear elasto-plastic dynamics. [less ▲] Detailed reference viewed: 56 (8 ULg)A New Energy-Dissipative Momentum-Conserving Time Integration Scheme Using the Variational Updates Framework. Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe (2007) Although they are the most widely used time integration algorithms for finite-element discretizations, algorithms based on the Newmark family are numerically stable only for linear models. To overcome ... [more ▼] Although they are the most widely used time integration algorithms for finite-element discretizations, algorithms based on the Newmark family are numerically stable only for linear models. To overcome that drawback, researches have recently focused on time integration algorithms stable in the non-linear range, leading to the development of Energy Momentum Conserving Algorithms or EMCA. A new Energy Momentum Conserving Algorithm was recently presented by the authors for elasto-plastic material models. This algorithm is based on a variational formulation of elasto-plastic updates for which the stress tensor always derives from an incremental potential, even when plastic behavior is considered. In this work this formalism is used to develop Energy-Dissipative Momentum-Conserving time integration algorithms, which have property of being stable in non-linear range, but also dissipate high-frequency numerical modes to improve the convergence properties. Using the potential existence of the variational updates framework, the verification of the numerical dissipation of energy in the non-linear range can easily be demonstrated. [less ▲] Detailed reference viewed: 50 (6 ULg)An Energy-Dissipative Momentum-Conserving Time Integration Algorithm for Viscoplastic Hyperelastic Models Based on the Variational Updates Framework Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe (2007) Traditional time integration algorithms for finite-element discretization are numerically stable only for linear models. To overcome that drawback, a new class of "Energy Momentum Conserving Algorithms ... [more ▼] Traditional time integration algorithms for finite-element discretization are numerically stable only for linear models. To overcome that drawback, a new class of "Energy Momentum Conserving Algorithms" or EMCA and ``Energy-Dissipative Momentum-Conserving'' or EDMC algorithms, verifying the conservation/dissipation laws in the non-linear range, was recently developed. They consist in a mid-point scheme with an adequate evaluation of the internal forces, which strongly assume the existence of an energy potential. Following the variational visco-plastic constitutive updates formalism, a general energy-dissipative momentum-conserving algorithm for hyperelastic-based formulation is proposed. The main feature of this variational formulation is that the stress tensor always derives from an incremental potential, even if plastic deformations occur, allowing to use it in the above integration algorithms. [less ▲] Detailed reference viewed: 41 (7 ULg)A variational formulation of constitutive models and updates in non-linear finite viscoelasticity ; Ponthot, Jean-Philippe ; Stainier, Laurent in International Journal for Numerical Methods in Engineering (2006), 65(11), 1831-1864 The purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a ... [more ▼] The purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a minimum principle within each load increment. The set of internal variables is strain-based and employs, according to the specific model chosen, a multiplicative decomposition of strain into elastic and viscous components. The present approach shares the same technical procedures used for analogous models of plasticity or viscoplasticity, such as the Solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration. However. instead of using the classical decomposition of inelastic strains into amplitude and direction, we take advantage of a spectral decomposition that provides additional facilities to accommodate, into simple analytical expressions, a wide set of specific models. Moreover, appropriate choices of the constitutive potentials allow the reproduction of other formulations in the literature. The final part of the paper presents a set of numerical examples in order to explore the characteristics of the formulation as well as its applicability to usual large-scale FEM analyses. Copyright (c) 2005 John Wiley [less ▲] Detailed reference viewed: 23 (1 ULg)Simulation of crashworthiness problems with improved contact algorithms for implicit time integration Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in International Journal of Impact Engineering (2006), 32(5), 799-825 When studying crashworthiness problems, contact simulation can be the source of a number of problems. A first one is the discontinuities in the normal evolution for a boundary discretized by finite ... [more ▼] When studying crashworthiness problems, contact simulation can be the source of a number of problems. A first one is the discontinuities in the normal evolution for a boundary discretized by finite elements. Another problem is the treatment of the contact forces that can introduce numerical energy in the system. In this paper, we propose to combine a method of discontinuity smoothing with the energy-momentum consistent scheme that recently appeared in the literature. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 48 (6 ULg)An energy momentum conserving algorithm using the variational formulation of visco-plastic updates Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in International Journal for Numerical Methods in Engineering (2006), 65(6), 904942 In this paper we use the variational formulation of elasto-plastic updates proposed by Ortiz and Stainier (Comput. Methods Appl. Mech. Eng. 1999; 171:419-444) in the context of consistent time integration ... [more ▼] In this paper we use the variational formulation of elasto-plastic updates proposed by Ortiz and Stainier (Comput. Methods Appl. Mech. Eng. 1999; 171:419-444) in the context of consistent time integration schemes. We show that such a formulation is well suited to obtain a general expression Of energy momentum conserving algorithms. Moreover, we present numerical examples that illustrate the efficiency of our developments. Copyright (c) 2005 John Wiley [less ▲] Detailed reference viewed: 32 (7 ULg)Energy conserving balance of explicit time steps to combine implicit and explicit algorithms in structural dynamics Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in Computer Methods in Applied Mechanics & Engineering (2006), 195(19-22), 21692192 Recent developments have proved the advantage of combining both time implicit and time explicit integration algorithms in structural dynamics. A major problem is to define the initial conditions for the ... [more ▼] Recent developments have proved the advantage of combining both time implicit and time explicit integration algorithms in structural dynamics. A major problem is to define the initial conditions for the implicit simulation on the basis of a solution obtained from an unbalanced explicit resolution. The unbalanced nature of the explicit algorithm leads to oscillations in the fields of interest. Therefore, the values obtained after an explicit computation cannot be used directly as initial conditions for an implicit simulation. In this paper, we develop such initial values that lead to a stable (no numerical creation of energy) and energy-conserving transition. (c) 2005 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 51 (8 ULg)A viscoelastic formulation for finite strains: application to brain soft tissues ; Ponthot, Jean-Philippe ; et al in Proceedings of XXVII CILAMCE – Iberian Latin American Congress on Computational Methods in Engineering (2006) Detailed reference viewed: 24 (1 ULg)Simulation of complex impact problems with implicit time algorithms: Application to a turbo-engine blade loss problem Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in International Journal of Impact Engineering (2005), 32(1-4), 358386 Recent developments, in non-linear structural dynamics, have led to a new kind of implicit algorithms: the energy-momentum conserving algorithm (EMCA) and the energy-dissipative, momentum-conserving ... [more ▼] Recent developments, in non-linear structural dynamics, have led to a new kind of implicit algorithms: the energy-momentum conserving algorithm (EMCA) and the energy-dissipative, momentum-conserving algorithm. Contrarily to commonly used algorithms, such as the explicit central difference or the alpha-generalized method, the stability of those algorithms is always ensured in the non-linear range. Thanks to this unconditional stability the only requirement on the time step size is that it must be small enough to capture the physics. This requirement is less restrictive than a conditional stability. In previous works, we have developed a new formulation of the internal forces for a hypoelastic model, that leads to an EMCA. In this paper, we will extend this formulation to an energy-dissipative, momentum-conserving algorithm. We will prove with an academic example, that our algorithm is more accurate than the alpha-generalized method in the non-linear range. Then we will simulate a blade loss problem to demonstrate the efficiency of our developments on complex dynamics simulations. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 46 (3 ULg)Simulation of Complex Crashworthiness Problems by Using a Combined Implicit/Explicit Time Integration. Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe (2005) In this work we will combine the ®-generalized explicit time integration scheme with the Energy-Dissipating Momentum-Conserving (EDMC) implicit time-integration scheme. Detailed reference viewed: 14 (1 ULg)A variational framework for nonlinear viscoelastic models in finite deformation regime ; Ponthot, Jean-Philippe ; Stainier, Laurent in Journal of Computational & Applied Mathematics (2005), 215(2), 400-408 This work presents a general framework for constitutive viscoelastic models in the finite deformation regime. The approach is qualified as variational since the constitutive updates consist of a ... [more ▼] This work presents a general framework for constitutive viscoelastic models in the finite deformation regime. The approach is qualified as variational since the constitutive updates consist of a minimization problem within each load increment. The set of internal variables is strain-based and uses a multiplicative decomposition of strain in elastic and viscous components. Spectral decomposition is explored in order to accommodate, into analytically tractable expressions, a wide set of specific models. Moreover, it is shown that, through appropriate choices of the constitutive potentials, the proposed formulation is able to reproduce results obtained elsewhere in the literature. Finally, numerical examples are included to illustrate the characteristics of the present formulation. (C) 2007 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 24 (9 ULg)A variational formulation of constitutive models and updates in nonlinear finite viscoelasticity ; Stainier, Laurent ; Ponthot, Jean-Philippe in 7ème Colloque National en calcul des Structures (2005) Detailed reference viewed: 14 (3 ULg)A variational framework for nonlinear viscoelastic and viscoplastic models in finite deformation regime Stainier, Laurent ; ; Ponthot, Jean-Philippe in MECOM 2005, , Mecanica Computational (2005) Detailed reference viewed: 24 (2 ULg) |
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