Optimization of a stabilized X-FEM formulation for frictional cracks

Numerical Meth Engineering

et al. 2013

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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...

Section: Large Time Increment Methodsmentioning

confidence: 99%

Section: Stage Then Local Stage Consists In Findingmentioning

confidence: 99%

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

Giacoma

Dureisseix

Numerical Meth Engineering

et al. 2013

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“…Different values for the normal and tangential problem can be chosen. These values influence only the convergence rate and optimal values are related to mechanical properties of the studied body [47,61,69,70]. According to [69], close-to-optimum values are searched as follows:…”

Section: Formulation Of the Latin-pgd For Frictional Contact Problemsmentioning

confidence: 99%

Toward an optimal a priori reduced basis strategy for frictional contact problems with LATIN solver

Giacoma

Dureisseix

Computer Methods in Applied Mechanics and Engineering

et al. 2015

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In this paper, an efficient a priori model reduction strategy for frictional contact problems is presented. We propose to solve this problem by using the finite element method and the non-linear LATIN solver. Basically, this non-linear solver assumes a space-time separated representation presaging nowadays PGD strategies. We extend this family of solvers to frictional engineering applications with reduced subspaces and no prior knowledge about the solution (contrary to a posteriori model reduction techniques). Hereinafter, a hybrid a priori/a posteriori LATIN-PGD formulation for frictional contact problems is proposed. Indeed, the suggested algorithm may or may not start with an initial guess of the reduced basis and is able to enrich the basis in order to reach a given level of accuracy. Moreover, it provides progressively the solution of the considered problem into a quasi-optimal space-time separated form compared to the singular value decomposition (SVD). Some examples are provided in order to illustrate the efficiency and quasi-optimality of the proposed a priori reduced basis LATIN solver.

“…The introduction of the X-FEM discretization of the fields and the conditions introduced by the stabilization process [24] lead to the discretized linear system (25). A priori formula were recently proposed to set up the parameters controlling the convergence rate (search direction and stabilization parameter) to obtain the best convergence rate possible [27] and improve the method efficiency by reducing the computing time.…”

Section: X-fem Discretization and Nonlinear Solver Dedicated To Interfacial Frictional Contactmentioning

confidence: 99%

2D fatigue crack propagation in rails taking into account actual plastic stresses

Trollé

Baietto

Engineering Fracture Mechanics

et al. 2014

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Due to increase axle loads, repeated passages of the wheels, rolling contact fatigue cracks initiate in the surface or subsurface of the rails. These defects can propagate and lead to the rail failure. A two-scale frictional contact fatigue crack model developed within the X-FEM framework is used to address the cracked rail problem, calculate the stress intensity factors, perform crack propagation and fatigue life prediction. Actual plastic stresses, quantified through a dedicated software developed by SNCF within the consortium IDR2, are taken into account in the propagation simulation via projection of the asymptotic mechanical fields. The effects of those actual plastic stresses are investigated on the crack growth path and rate. Interactions between multiple cracks of a network are also analyzed.