Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

Biotteau, Ewen; Gravouil, Anthony; Lubrecht, Antonius; Combescure, Alain

doi:10.1007/s00466-011-0628-z

Cited by 9 publications

(6 citation statements)

References 21 publications

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“…The non-intrusivness is preserved even when the crack propagates and when the shape of doamin of the local model evolves As a short term perspective, it could be interesting to used such a method to truly couple a real commercial FEA software and a reasearch piece of code, as it was done in [12]. As mentionned before, another extension of this work would be to develop an adaptativity of the grid hierarchy, following [6].…”

Section: Resultsmentioning

confidence: 98%

Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver

et al. 2013

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A Local/Global non-intrusive coupling algorithm is proposed for the analysis of mixed-mode crack propagation. It is based on a three scale multigrid and extended finite element method, that was proposed recently for the direct estimation of stress intensity factors of static cracks. The algorithm couples a linear elastic global model (possibly performed by a industrial software) with an enhanced local model capable of modeling a crack and accurately estimating SIFs (performed by a separate research code). It is said non-intrusive since it does not modify the global mesh, its connectivity and solver. For the global model, the contribution of the local patch consists in additional nodal efforts near the crack, which makes it compatible with most softwares. Further the shape of the domain over which the local model is applied is automatically adapted during propagation.Keywords nested models · mixed mode · localized multigrid · williams · stress intensity factors 1 IntroductionThe question of the inclusion of a crack and its propagation in a finite element model initially not expected for this, is a question which is still today the subject of numerous

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Section: Resultsmentioning

confidence: 98%

Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver

et al. 2013

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“…Then, both of the global and local problems are coupled. Other efficient approaches are multigrid solvers suitable for various nonlinear problems [37][38][39][40]. For frictional contact problems, multigrid methods were proposed in [22].…”

Section: Efficient Resolution Using Reduced-order Modelmentioning

confidence: 99%

A multiscale large time increment/FAS algorithm with time‐space model reduction for frictional contact problems

Giacoma

Dureisseix

Gravouil

et al. 2013

Numerical Meth Engineering

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A multiscale strategy using model reduction for frictional contact computation is presented. This new approach aims to improve computation time of finite element simulations involving frictional contact between linear and elastic bodies. This strategy is based on a combination between the LATIN (LArge Time INcrement) method and the FAS multigrid solver. The LATIN method is an iterative solver operating on the whole time-space domain. Applying an a posteriori analysis on solutions of different frictional contact problems shows a great potential as far as reducibility for frictional contact problems is concerned. Timespace vectors forming the so-called reduced basis depict particular scales of the problem. It becomes easy to make analogies with multigrid method to take full advantage of multiscale information. A. GIACOMA ET AL. in large-scale elasticity problems with contact and friction. Once again, because of the nonsmooth property of contact problems, convergence proof of generalized Newton's methods are hard to provide. Another method consists in casting the contact problems into a linear complementarity problem (LCP) and using specific solvers such as active-set methods, Lemke's algorithm, projected successive over relaxation. In [20], an LCP formulation is used to solve a frictional contact problem by faceting the Coulomb's cone. Nevertheless, this approximation is tough and not efficient (the problem to solve becomes larger). Nowadays, LCP formulations are suited to frictionless problems.Generally speaking, and even within a quasi-static context, all these nonlinear solvers can lead to prohibitive time of computations. Acceleration strategies based on multigrid methods were proposed [21,22]. Computational costs spur recent and intensive works on efficient model reduction techniques in various fields [23][24][25][26]. But because of the nondifferentiable nature of frictional contact, application of such methods seems to be heretic.The aim of this work is to propose a strategy accelerating solution for frictional contact problems in the finite element framework, embedding model reduction techniques also well-suited for parametric studies. Linear elastic, homogeneous, isotropic behavior, and quasi-static evolution are assumed for the bodies. Frictional contact laws involve a nonlinear and nonsmooth behavior at the boundary of the body. To solve this mechanical problem, the nonincremental LArge Time INcrement (LATIN) method is used. This method is well-known for its ability to solve difficult nonlinear large problems (nonlinear material, contact problems...) [27,28] with a global time-space approach. This method is closed to augmented Lagrangian methods. Its great advantages are non refactorization of matrices (stiffness matrix remains constant through LATIN iterations) and explicit subsequent iterations (no iterations to handle the nonlinear behavior solved only on the contacting boundary). So the cost of a LATIN iteration is low even if the number of iterations can be elevated as augmented Lagrangian method...

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“…Furthermore, the extension of dual HATI (macro and micro) to variational integrators has to be studied in detail as the bridge between α ‐schemes and variational approaches is rather small. Some attempts to use dual HATI to space–time localized multi‐grid approaches seem also very interesting when coupled with space–time error indicators . Finally, dual HATI have also been applied recently with success to FSI and co‐simulations, and many extensions to multi‐physics in general have to be considered.…”

Section: Discussionmentioning

confidence: 99%

Heterogeneous asynchronous time integrators for computational structural dynamics

Gravouil

Combescure

Brun

2014

Numerical Meth Engineering

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SUMMARYComputational structural dynamics plays an essential role in the simulation of linear and nonlinear systems. Indeed, the characteristics of the time integration procedure have a critical impact on the feasibility of the calculation. In order to go beyond the classical approach (a unique time integrator and a unique timescale), the pioneer approach of Belytschko and co-workers consisted in developing mixed implicit-explicit time integrators for structural dynamics. In a first step, the implementation and stability analyses of partitioned integrators with one time step have been achieved for a large class of time integrators. In a second step, the implementation and stability analyses of partitioned integrators with different time steps were studied in detail for particular cases. However, stability results involving different time steps and different time integrators in different parts of the mesh is still an open question in the general case for structural dynamics. The aim of this paper is to propose a state-of-the art of heterogeneous (different time schemes) asynchronous (different time steps) time integrators (HATI) for computational structural dynamics. Finally, an alternative approach based on energy considerations (with velocity continuity at the interface) is proposed in order to develop a general class of HATI for structural dynamics.

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Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

Abstract: International audienc

Cited by 9 publications

References 21 publications

Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver

Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver

A multiscale large time increment/FAS algorithm with time‐space model reduction for frictional contact problems

Heterogeneous asynchronous time integrators for computational structural dynamics

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