François Bay

Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria

Modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics. Three different crack growth criteria and the respective crack paths prediction for several test cases are compared. The maximal circumferential stress criterion, the strain energy density fracture criterion and the criterion of the maximal strain energy release rate are implemented using advanced finite element techniques. A fully automatic remesher enables to deal with multiple boundaries and multiple materials. The propagation of the crack is calculated with both remeshing and nodal relaxation. Several examples are presented to check for the robustness of the numerical techniques, and to study specific features of each criterion.

Crack propagation modelling using an advanced remeshing technique

The modelling of a crack propagation through a finite element mesh is of prime importance in fracture mechanics. We propose here a solution based on an advanced remeshing technique. A fully automatic remesher enables us to deal with multiple boundaries and multiple materials. The propagation of the crack is achieved with both remeshing and nodal relaxation. A maximal normal stress criterion is used to compute the crack direction. Several tools are developed and presented to obtain accurate results at the crack tip: evolving mesh refinement, crack tip finite elements, ring of elements surrounding the crack. Finally, several applications are presented to show the robustness of this technique.

Induction heating processes optimization a general optimal control approach

A general automatic optimization procedure coupled to a finite element induction heating process simulation has been developed. The mathematical model and the numerical methods are presented along with results validating the model. The first part of this paper presents the direct induction heating mathematical model, the related main numerical choices and especially the ultra-weak coupling procedure. The general optimization problem is then presented with the full detailed transposition of the ultra-weak coupling procedure to the adjoint problem. Numerical results provided at the end prove the efficiency and robustness of the adjoint model in optimizing induction heating processes.

Thermomechanics of the cooling stage in casting processes: Three-dimensional finite element analysis and experimental validation

A thermomechanical three-dimensional (3-D) finite element analysis of solidification is presented. The heat transfer model is based on a multidomain analysis accounting for noncoincident meshes for the cast part and the different mold components. In each subdomain, a preconditioned conjugate gradient solver is used. The mechanical analysis assumes the mold is rigid. A thermoelastic-viscoplastic rheological model is used to compute the constrained shrinkage of the part, resulting in an effective local air gap width computation. At each time increment, a weak coupling of the heat transfer and mechanical analyses is performed. Comparisons of experimental measurements and model predictions are given in the case of a hollow cylindrical aluminum alloy part, showing a good quantitative agreement. An application to an industrial aluminum casting is presented, illustrating the practical interest of thermomechanical computations in solidification analysis.

Identification of magnetic parameters by inverse analysis coupled with finite-element modeling

We present a new approach for identification of the material electromagnetic parameters that are involved in electrothermal process simulations. We use inverse analysis techniques coupled with an induction heating finite-element model (FEM) and software developed in our laboratory. We describe here the direct induction heating FEM, the physical formulations, and the iterative identification procedure, and then present numerical tests and results.

Three-dimensional finite element modelling for soft tissues surgery

Abstract Laparoscopy is a surgical technique that requires fine control from the surgeon point of view. Up to this day, this experience can only be obtained by intensive training. That is why a lot of training simulators have been developed in the medical area. We present here a new approach based on a three-dimensional finite element software and an elastic constitutive equation, able to predict realistic results. This software has been applied to soft tissues deformation, namely lamb kidney and human uterus, and the numerical results are compared to experimental ones.

An innovative strategy to create equivalent elements for modelling assembly points in joined structures

Purpose – Large structures (e.g. plane, bridge, etc.) often include several hundreds of assembly points. Structural computations often use over-simplistic approximations for these points; among others, they do not take into account the thermo-mechanical history due to the assembling process. Running computations with each assembly point modelled completely would require too much time to achieve a simulation. There is thus a need to create equivalent elements for assembly points in order to: take into account the mechanical state of the assembly point in the design stage – while reducing the computational time cost at the same time. This paper aims to discuss these issues. Design/methodology/approach – This paper introduces an innovative strategy based on a coupling procedure between a finite element tool for modelling the assembly process in order to access to the mechanical state of the assembly point and an optimisation algorithm, in order to identify the equivalent element parameters. Findings – The st...

Numerical stability analysis and flow simulation of lid-driven cavity subjected to high magnetic field

In this work, we study the flow of a conducting fluid inside a two-dimensional square domain. The problem is solved by using a variational multiscale finite element approach. The study focuses on a high magnetic interaction parameter range and high Reynolds number. Under the imposition of a high magnetic field, the flow gets regularized, but fast transient phenomena take place, which could lead to numerical errors. An expression to compute the maximum time step that guarantees convergence in explicit schemes is proposed and validated through numerical tests.

An elastic‐viscoplastic finite element model for multimaterials

A finite element model for multimaterial configurations is presented. The material behavior of each body within a composite material is given by an elastic‐viscoplastic constitutive law. Automatic remeshing techniques which preserve the topology of the different bodies of material are used to simulate large deformations of the multiphasic system. An experimental set‐up has been designed in order to simulate the compaction of multilayer composite materials. Plasticine was chosen as a model material. Experimental results are used to validate the finite element model for consolidation of multilayer composites.

Electromigration-induced failure in operando characterization of 3D interconnects: microstructure influence

An accurate knowledge of the phenomenon is required to develop a predictive modeling of the electromigration failure. Thus, a hitherto unseen SEM in operando observation method is devised. The test structure with “high density” through silicon vias (TSV) is tested at 623 K with an injected current density of 1 MA/cm2. Regular shots of micrographs inform about the voids nucleation, forced in copper lines above the TSV, and about the scenario of their evolution. A clear relation is established between voids evolution and the one of the electrical resistance. The lack of impact of test conditions on the failure mechanism is demonstrated. Finally, the impact of microstructure on the depletion mechanism is discussed. Grain boundaries are preferential voids nucleation sites and influence the voids evolution. A probable effect of grain size and crystallographic orientation is revealed.