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See detailA robust preconditioning technique for the extended finite element method
Menk, A.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2011), 85(13), 1609-1632

The extended finite element method enhances the approximation properties of the finite element space by using additional enrichment functions. But the resulting stiffness matrices can become ill ... [more ▼]

The extended finite element method enhances the approximation properties of the finite element space by using additional enrichment functions. But the resulting stiffness matrices can become ill-conditioned. In that case iterative solvers need a large number of iterations to obtain an acceptable solution. In this paper a procedure is described to obtain stiffness matrices whose condition number is close to the one of the finite element matrices without any enrichments. A domain decomposition is employed and the algorithm is very well suited for parallel computations. The method was tested in numerical experiments to show its effectiveness. The experiments have been conducted for structures containing cracks and material interfaces. We show that the corresponding enrichments can result in arbitrarily ill-conditioned matrices. The method proposed here, however, provides well-conditioned matrices and can be applied to any sort of enrichment. The complexity of this approach and its relation to the domain decomposition is discussed. Computation times have been measured for a structure containing multiple cracks. For this structure the computation times could be decreased by a factor of 2. © 2010 John Wiley & Sons, Ltd. [less ▲]

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See detailInfluence of the microstructure on the stress state of solder joints dusing thermal cycling
Menk, A.; Bordas, Stéphane UL

in Proceedings of 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009 (2009)

The lifetime of a solder joint is mainly determined by its creep behaviour. Creep arises from the stresses inside the solder joints as a consequence of the thermomechanical mismatch of the board and the ... [more ▼]

The lifetime of a solder joint is mainly determined by its creep behaviour. Creep arises from the stresses inside the solder joints as a consequence of the thermomechanical mismatch of the board and the substrate. The stress state is heavily influenced by the anisotropy of tin. To understand the damage process in solder joints, the influence of the anisotropic microstructure must be understood. In this paper the influence of different grain sizes, shapes and orientations on the stress state is evaluated, based on numerical experiments. [less ▲]

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