Eric Béchet

Re-meshing algorithms applied to mould filling Simulations in resin transfer moulding

In injection moulding processes such as Resin Transfer Moulding (RTM) for example, numerical simulations are usually performed with a fixed mesh, on which the displacement of the flow front is predicted by the numerical algorithm. During the injection, special physical phenomena occur on the front, such as capillary effects inside the fibre tows or heat transfer when the fluid is injected at a different temperature than the mould. In order to approximate these phenomena accurately, it is always better to adapt the mesh to the shape of the flow front. This can be achieved by implementing re-meshing algorithms, which will provide not only more accurate solutions, but also faster calculations. In order to represent precisely the shape of the saturated domain in the cavity, the mesh needs to be non-isotropic in the vicinity of the flow front. The size of the elements along the front is connected to the overall accuracy needed for the simulation; the size in the perpendicular direction governs the accuracy on the position of the moving boundary in time. Since these two constraints on element size are not related, the need for non-isotropic mesh refinement is crucial. In the approach proposed here, the mesh is changed at each time step from a background isotropic mesh used as starting point in the refinement algorithm. The solution needs to be projected on the new mesh after each re-meshing. This amounts to adopting a new filling algorithm, which will be validated by comparison to a standard simulation (without re-meshing) and with experimental data.

Crack Lip Contact Modeling Based on Lagrangian Multipliers with X-FEM

The eXtended Finite Element Method (X-FEM), developed intensively in the past 15 years has become a competitive tool for the solution of problems with evolving discontinuities and singularities. In the present study, we focus on the application of X-FEM on frictionless contact problems in the context of fracture mechanics. A promising approach in the literature counting for this problem consists in applying Lagrangian multipliers. Meanwhile, as pointed out in Ji and Dolbow (Int J Numer Methods Eng 61:2508–2535, 2004), a naive choice for Lagrangian multiplier space leads to oscillatory multipliers on the contact surface. This oscillation results from a non-uniform but mesh-dependent inf-sup condition. In this work, we adapt the algorithm proposed in Bechet et al. (Int J Numer Methods Eng 78:931–954, 2009) on crack lip contact by discretizing the displacement field with both scalar and vector tip enrichment functions (Chevaugeon et al., Int J Multiscale Comput Eng 11:597–631, 2013). The influence of the tip enrichment functions on the stability of the formulation is addressed. We show evidences that the vector enrichment functions can improve the conditioning of the problem without jeopardizing the simulation accuracy in the presence of contact.

Some Numerical Studies with X-FEM for Cracked Piezoelectric Media

Piezoelectric materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the extended finite element method (X-FEM) has been gained much attention to model cracks in structural materials. This paper presents the application of X-FEM to the coupled electromechanical crack problem in two-dimensional piezoelectric structures. The convergence of solutions is investigated in the energy norm and for the stress intensity factors. Then, some studies about inaccuracies in the stresses near the crack tip are reported.

Explicit dynamic with X-FEM to handle complex geometries

Although the calculation capacities have considerably increased these last years, the complexity of the numerical simulations in dynamic fields still induce many problems, essentially due to CPU time calculation. For instance, the use of explicit scheme yields a critical time step. It depends on the greatest structure eigenvalue [1], [2]. Commonly, rather than to identify this eigenvalue, an upper approximation computed corresponds to the smaller characteristic size (if all elements share the same behavior). These critical time steps are usually induced by mesh constraints. For complex geometries, very small sized elements may arise. One approach is then to optimize the mesh by removing elements or by using mass scaling to improve the critical time step.