Local adaptive refinement method for the fracture of heterogenous materials
Résumé
In order to anticipate problems with aging nuclear power plants, the French ’Institut
de Radioprotection et de Sûreté Nucléaire’ (IRSN) studies microstructural evolution of
concrete (confinement structures) and of metallic components (reactor vessel, vessel
wall, steam generator). The issues linked to the aging of these materials can be studied
through micromechanical methods based on the Finite Element numerical method. In
this case, very fine meshes have to be used to take into account heterogeneities at the
scale of the structure. A solution to reduce the associated computational costs is to
perform local adaptiv mesh refinement involving refinement criteria which depend on
the studied physics.
The refinement method used in this study is called ’CHARMS’ (Conforming Hierarchical
Refinement MethodS) and is based on the refinement/unrefinement of the basis
functions rather than the refinement of the finite elements and thus allows nonconformities
[1]. These nonconformities are geometrical and not linked to spatial discretization :
the approximation spaces remain H1-conform.
Combining a local refinement criteria as critical value of the Von-Mises equivalent
stress to the CHARMS method enables to perform refinement where heterogeneities
linked to the chosen criteria are the most marked. Namely in the case of heterogenous
material this method is able to capture the local heterogeneity of the stress field between
two phases. An application to numerical concrete loaded in traction will be presented
showing the local mesh refinement around aggregates and microstructures.