On energy consistency of large deformation plasticity models, with application to the design of unconditionally stable time integrators

Meng, X.N.; Laursen, Tod A.

doi:10.1016/s0168-874x(02)00087-2

Cited by 11 publications

(12 citation statements)

References 13 publications

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“…First, it is of interest to develop energy and momentum consistent formulations for dynamic finite strain plasticity. Again the MPM algorithm can take advantage of developments in this area for the finite element grid dynamics [34], [35]. Another promising area is the simulation of Newtonian fluid dynamics, possibly with fluid-structure interaction.…”

Section: Closurementioning

confidence: 99%

An unconditionally stable, energy–momentum consistent implementation of the material-point method

Love

Sulsky

2006

Computer Methods in Applied Mechanics and Engineering

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The Center for High Performance Computing (HPC@UNM) provides a focus for high performance computing and communication at the University of New Mexico (UNM). HPC@UNM is committed to innovative research in computational and computer science with emphasis on both algorithm development and application. As part of this commitment, HPC@UNM sponsors this technical report series. The technical reports are subject to internal review by HPC@UNM. However, the material, as presented, does not necessarily reflect any position of HPC@UNM. Further, neither UNM, nor the HPC, makes any warranty or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information contained in this report. Abstract Conservation of linear and angular momenta, and conservation of energy are examined for the material-point method (MPM). It is shown that MPM can be formulated with implicit energy and momentum conserving mesh dynamics for hyperelastic materials. With a consistent mass matrix the resulting overall numerical method preserves the conservative properties of the mesh solution. Energy dissipation and angular momentum errors are also quantified for a lumped mass formulation. Properties of the method are illustrated in numerical examples.

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Section: Closurementioning

confidence: 99%

An unconditionally stable, energy–momentum consistent implementation of the material-point method

Love

Sulsky

2006

Computer Methods in Applied Mechanics and Engineering

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“…But when using a larger time step t = 20 ms, if the solution obtained with the EMCA algorithm (Figure 12(a)) remains similar that the one with t = 2.5 ms, the solution obtained with Newmark algorithm is quite different Figure (12(b)). If we analyse the time evolution of the energy that is plastically dissipated (Figure 13(a)) with a time step equal to t = 20 ms, it appears that the EMCA algorithm gives the same solution than those obtained by Meng and Laursen [10] and with an hypo-elastic model [12]. The Newmark solution diverges after a few ms to reach a 100% error.…”

Section: Numerical Example 3: Impact Of Two Cylindersmentioning

confidence: 79%

“…Reference [35]). It was also studied in the framework of consistent time algorithms for hyper-elastic based elasto-plastic models by Meng and Laursen [10], and in the framework of consistent time algorithms for hypo-elastic based elasto-plastic models by Noels et al [12] . In this paper we compare previous results with Figure 6.…”

Section: Numerical Example 2: Taylor's Bar Impactmentioning

confidence: 99%

“…Frictionless contact is treated with the consistent method proposed by Armero and Petöcz [14]. This example was first proposed by Meng and Laursen [10] in the framework of consistent time algorithm for hyper-elastic based elasto-plastic models, and was also studied by Noels et al [12] in the framework of consistent time algorithm for hypo-elastic based elasto-plastic models. In this paper, we compare previous results with We will compare results obtained with the following constant time step sizes: 20, 10, 5 and 2.5 ms.…”

Section: Numerical Example 3: Impact Of Two Cylindersmentioning

confidence: 99%

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An energy momentum conserving algorithm using the variational formulation of visco‐plastic updates

Noels¹,

Stainier²,

Ponthot³

2005

Numerical Meth Engineering

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SUMMARYIn 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.

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“…Energy-momentum conserving algorithms were then developed by Meng and Laursen [14,15] in such a way that the work of internal forces is dissipative, consistently with plastic behavior. They were also developed by Noels et al [16,17] and Armero [18] in such a way that for respectively hypo-elastic and hyper-elastic based elasto-plastic materials, the work of internal forces corresponds to the change of reversible energy plus the plastically dissipated energy.…”

Section: Introductionmentioning

confidence: 99%

A first-order energy-dissipative momentum-conserving scheme for elasto-plasticity using the variational updates formulation

Noels¹,

Stainier²,

Ponthot³

2008

Computer Methods in Applied Mechanics and Engineering

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In a previous paper (Int. J. for Numer. Meth. in Eng. 2006; 65:904-942) 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 momentumconserving time integration algorithm for elasto-plasticity.

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On energy consistency of large deformation plasticity models, with application to the design of unconditionally stable time integrators

Cited by 11 publications

References 13 publications

An unconditionally stable, energy–momentum consistent implementation of the material-point method

An unconditionally stable, energy–momentum consistent implementation of the material-point method

An energy momentum conserving algorithm using the variational formulation of visco‐plastic updates

A first-order energy-dissipative momentum-conserving scheme for elasto-plasticity using the variational updates formulation

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