A direct method for the solution of evolution problems

Comte, François; Maïtournam, Habibou; Burry, Pierre; Nguyen, Thi Mac Lan

doi:10.1016/j.crme.2006.02.007

Cited by 10 publications

(4 citation statements)

References 4 publications

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“…This type of problem was solved in [20] by introducing "micro/macro projectors" among grids. Some works have been devoted to the treatment of periodic loading histories [1,13,15,30,36,46,49].…”

Section: Justificationmentioning

confidence: 99%

Proper Generalized Decomposition for Multiscale and Multiphysics Problems

Néron

Ladevèze

2010

Arch Computat Methods Eng

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This paper is a review of the developments of the Proper Generalized Decomposition (PGD) method for the resolution, using the multiscale/multiphysics LATIN method, of the nonlinear, time-dependent problems ((visco)plasticity, damage, . . . ) encountered in computational mechanics. PGD leads to considerable savings in terms of computing time and storage, and makes engineering problems which would otherwise be completely out of range of industrial codes accessible.

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Section: Justificationmentioning

confidence: 99%

Proper Generalized Decomposition for Multiscale and Multiphysics Problems

Néron

Ladevèze

2010

Arch Computat Methods Eng

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“…The feasibility of the LATIN method is tested within a large number of cycles in the case of viscoplasticity. More recently, Comte et al [16] presented an alternative numerical method to solve the structural evolution problem. The method issued from two methods, LATIN and wavelet transform.…”

Section: Introductionmentioning

confidence: 99%

A mixed PGD-a priori time basis strategy for the simulation of cyclic transient thermal behavior

Takash

Béringhier

Hammoud

et al. 2020

Mechanics & Industry

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The knowledge of the service life of polymers under cyclic loading, widely used in industrial applications, is required and usually based on the use of methods necessitating an accurate prediction of the stabilized cycle. This implies a large computation time using the Finite Element Method (FEM) since it requires a large number of cycles for polymers. To alleviate this difficulty, a model order reduction method can be used. In this paper, a mixed strategy is investigated. Through the Proper Generalized Decomposition Method (PGD) framework, this strategy combines the Fast Fourier Transform (FFT) to create a priori time basis and the FEM to compute the related spatial modes. The method is applied to 3D thermal problems under cyclic loadings. The robustness of the proposed strategy is discussed for various boundary conditions, multi-times, and different cyclic loadings. A large time saving is obtained proving the interest of this alternative strategy to deal with fatigue simulations.

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“…The reduced model is then used to compute a similar model or a model with a larger time interval. Other model reduction strategies have been addressed as the LArge Time INcrement method [11][12][13] or the A Priori HyperReduction [14]. But, these methods are restricted to a space-time representation.…”

Section: Introductionmentioning

confidence: 99%

A reduced simulation applied to the viscoelastic fatigue of polymers

Hammoud¹,

Béringhier²,

Grandidier³

2014

Comptes Rendus. Mécanique

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The paper extends the use of the PGD method to viscoelastic evolution problems described by a large number of internal variables and with a large spectrum of relaxation times. The internal variables evolution is described by a set of linear differential equations that involve many time scales. The feasibility and the robustness of the method are discussed in the case of a polymer in a non-equilibrium state under creep and cyclic loading. The relationships between different time scales (loading and internal variables) are also discussed.

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A direct method for the solution of evolution problems

Cited by 10 publications

References 4 publications

Proper Generalized Decomposition for Multiscale and Multiphysics Problems

Proper Generalized Decomposition for Multiscale and Multiphysics Problems

A mixed PGD-a priori time basis strategy for the simulation of cyclic transient thermal behavior

A reduced simulation applied to the viscoelastic fatigue of polymers

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