Jean-Michel Bergheau

A nonlinear elastic behavior to identify the mechanical parameters of human skin in vivo

Background/purpose: Various analyses have been performed to identify the mechanical properties of the human skin tissue in vivo. They generally use different approaches and hypotheses (behavior laws as well as mechanical tests) and the obtained results are consequently difficult to analyze and compare. In this paper, an inverse method that can be adapted to any kind of mechanical tests and behavior laws is presented.

Finite element simulation of heat transfer

Part 1: Steady conduction1. Mathematical formulation.2. The finite element method.3. Isoparametric elements.Part 2: Transient conduction, non-linearities, convective heat transfer4. Transient conduction.5. Non-linearites.6. Convective heat transfer.Part 3: Coupled problems7. Radiative heat transfer in cavities.8. Fluid-structure interaction in a pipe.9. Metallurgical phase change.10. Thermal and electrical phenomena.

Experimental and numerical study of the ploughing part of abrasive wear

Understanding and quantification of ploughing resistance and associated deformation is of primary importance for materials undergoing abrasive wear. The aim of this study is to understand mechanical phenomena induced by a ploughing process. A comparison of numerical simulation with experimental results has been performed in order to validate our numerical model. The process to be studied is the ploughing of a soft flat surface with a rigid sphere. A numerical study with a finite element code has been performed in order to understand the role of different parameters on strain and stress fields. First of all, we have studied the process in terms of applied loads and strained material but the material characteristics seemed to have a larger influence on the process than the boundary conditions themselves. A profilometric study on numerical simulations has shown us that the elastic strain was not totally recovered and gave rise to residual stresses. Moreover, a study of the contact surface and the ploughing friction coefficient has been developed and a comparison to Bowden and Tabor model has been made. It has shown us that strain hardening modeling has an essential influence on the ploughing friction coefficient. Thus, we have performed scratch test on an AISI316L stainless steel in order to validate our numerical results.

Coupling between finite elements and boundary elements for the numerical simulation of induction heating processes using a harmonic balance method

For the modeling of induction heating processes, strongly coupled magnetodynamic and thermal problems can be solved together within the same finite element. This is called the direct method. In this case, the electromagnetic quantities are expressed through Fourier series according to the harmonic balance method. In this paper, each harmonic is calculated in the whole space by using the coupling between finite elements and boundary elements. Especially suitable when moving parts are involved and because the mesh of air is unnecessary, it is shown that this coupling is still successful if the direct method is used. At the end, the efficiency of this approach is illustrated with an example.

A simple and robust moving mesh technique for the finite element simulation of Friction Stir Welding

The simulation of the Friction Stir Welding process is a complex problem which involves physical couplings between mechanics and heat transfer, very large deformations and strain rates in the stirring zone around the pin. To avoid mesh distortions or very large computing time due to the Arbitrary Lagrangian Eulerian technique usually proposed in the literature for the finite element method, a simple but robust moving mesh technique is proposed for the numerical modeling of the FSW process. It is based on a Eulerian formalism and the mesh is composed of 2 parts: a first one which is fixed around the stirring zone and a second one which includes the base material near the tool and moves with a rotational solid motion corresponding to the tools velocity. Therefore, there are no mesh distortions and the Eulerian formalism leads to satisfying computing time. An example clearly evidences the efficiency and robustness of the moving mesh technique proposed for a 3D complex geometry of the tool.

Resistance Spot Welding Process: Experimental and Numerical Modeling of the Weld Growth Mechanisms with Consideration of Contact Conditions

ABSTRACT To investigate the weld growth mechanisms in resistance spot welding, a fully coupled numerical and experimental approach has been performed using the finite-element method. This numerical model dedicated to the resistance welding simulation is presented in the first part of this article. To take the contact conditions carefully into account, a finite-element formulation is detailed in the second part, where the experimental device used to measure the interface contact properties is also presented. An example is detailed to validate the approach presented in this article. The experimental shape evolution of the nugget is compared to numerical results.

An Implicit Fixed-Grid Method for the Finite-Element Analysis of Heat Transfer Involving Phase Changes

The finite-element method is widely used for thermal numerical simulation of heat treatment, casting, or welding processes. The modeling of phase changes requires the simulation of highly nonlinear problems due to latent heat effects. In this article, a finite-element procedure is developed for modeling latent heat effects using an implicit time discretization for transient heat conduction problems involving phase changes for which the enthalpy can be supposed to be a function of temperature only. It is also developed for stationary convection-diffusion problems. Examples are presented to show the efficiency of the method for isothermal and anisothermal transformations. Finally, the method is extended to take couplings with metallurgical transformation kinetics into account.

Thermometallurgical and mechanical modelling of welding – application to multipass dissimilar metal girth welds

Abstract The prediction of welding residual stresses and distortions needs to take accurately account of the couplings between heat transfer, metallurgy and stresses–strains. The numerical simulation of multipass welding of dissimiliar metal including ferritic steels is specially difficult as three-dimensional (3D) simulation a priori needs to accurately take into account the complex phenomena in the heat affected zone and in the overlapping regions. The results obtained using a simplified two-dimensional axisymmetric model are discussed according to those resulting from a complete 3D simulation. It is shown that for multipass circular welds, 3D computations are mandatory to analyse overlapping regions but two-dimensional assumptions enable to capture stress distribution in the current region. Comparisons with experimental measurements of stresses using neutron diffraction or deep hole drilling are presented to validate the computed residual stresses.

Prediction of welding residual distortions of large structures using a local/global approach

Prediction of welding residual distortions is more difficult than that of the microstructure and residual stresses. On the one hand, a fine mesh (often 3D) has to be used in the heat affected zone for the sake of the sharp variations of thermal, metallurgical and mechanical fields in this region. On the other hand, the whole structure is required to be meshed for the calculation of residual distortions. But for large structures, a 3D mesh is inconceivable caused by the costs of the calculation. Numerous methods have been developed to reduce the size of models. A local/global approach has been proposed to determine the welding residual distortions of large structures. The plastic strains and the microstructure due to welding are supposed can be determined from a local 3D model which concerns only the weld and its vicinity. They are projected as initial strains into a global 3D model which consists of the whole structure and obviously much less fine in the welded zone than the local model. The residual distortions are then calculated using a simple elastic analysis, which makes this method particularly effective in an industrial context. The aim of this article is to present the principle of the local/global approach then show the capacity of this method in an industrial context and finally study the definition of the local model.

Numerical aspects of fluid infusion inside a compressible porous medium undergoing large strains

A new model for a thermo-reactive fluid flow across a highly compressible porous medium has been proposed and employed to predict infusion-based manufacturing processes for polymer composites (Celle, 2006). These techniques consist in mixing the reinforcements and the resin during the manufacturing cycle, transversely to the fabrics plane, by applying a pressure on the resin/preform stacking. This yields cost reductions and avoids filling problems. The introduction of a numerical model in a finite element software to study infusion-based processes will increase their diffusion by a reliable prediction of both part thickness and porosity (Celle et al., 2008). The present paper deals mainly with the numerical treatments related to the resin layer.