Anisotropic mesh adaptation for ductile damage and fracture modelling
Résumé
Automatic remeshing has been used for many years within the framework of materials forming processes to preserve the good quality of elements even for large plastic deformation. Automatic mesh adaptation, coupled with an appropriate error estimator, enables to optimize automatically the mesh size during the simulation to obtain accurate results in an efficient manner. The work presented here focuses on the use of anisotropic mesh adaptation for ductile damage and fracture mechanisms. First, a brief description of the construction of the anisotropic metric which is used to generate the anisotropic mesh adaptation is done. Then, the work focuses on three different aspects of damage and fracture: - Damage at the microscale: ductile damage is usually represented by voids nucleation, growth and coalescence at the microscale. The numerical modelling of these mechanisms is achieved using a level set framework. coupled with anisotropic mesh adaptation. It is shown how this numerical strategy enables the numerical modelling of voids growth for different configurations in an efficient way. - Damage to fracture transition at the macro scale: an anisotropic metric is built based on both ductile damage and damage rate. The elements of the mesh are particularly refined in the directions perpendicular to high gradients of damage. Using a simple kill-element technique with such an approach makes the damage to fracture transition quite easy to model with a minimum loss of volume. A cup-and-cone fracture is modelled to show the efficiency of this technique. - Fracture modelling: crack propagation is studied here in an implicit way, by using both levelset functions to localize the crack front and faces, and anisotropic mesh adaptation to capture singularities without enriching elements shape functions. With these three applications, it is shown that anisotropic mesh adaptation is a powerful tool to enhance the accuracy and efficiency of ductile damage and fracture modelling at different scales. References : [1] T. Coupez, H. Digonnet, R. Ducloux, Parallel meshing and remeshing, Appl. Math. Model., 25 (2), 153-175,(2000). [2] Y. Mesri, W. Zerguine, H. Digonnet, L. Silva, T. Coupez, Dynamic Parallel Adaption for Three Dimensional Unstructured Meshes: Application to Interface Tracking, Proceedings of the 17th International Meshing Roundtable, (2008). [3] M. Bernacki, Y. Chastel, T. Coupez, R.E. Logé, Level set framework for the numerical modelling of primary recrystallization in polycrystalline materials, Scripta Mater., 58, 1129-32, (2008). [4] R. El Khaoulani, Prédiction fiable de l'endommagement ductile par la méthode des éléments finis mixte : endommagement non local et adaptation de maillage, Ph.D. Mines ParisTech, 2010 (in french).