Controlling Physical Properties on Interfaces Using Parametrised Level Set Methods and Extended Finite Element Method

The stress field information states a main point of interest, when regarding structural optimisation of bimaterial structures. The introduction of stress criteria along the volume is crucial in the development of new designs. In the case of bimaterials, the stress field along the interface deserves additional attention e.g. to prevent delamination. Tracing the interface through shape optimisation in CAD‐based methods is rather expensive due to the high cost in remeshing techniques. Therefore, level set methods with fixed background meshes are used as in [1]. In this work an approach for controlling strains and stresses on the interface in a framework of shape optimisation is introduced. The geometry description is managed by parametrised level set functions and a sub‐meshing technique is coupled with the extended finite element method. The parametrisation with superellipses allows to reduce the number of design variables to a minimum of six variables per introduced ellipse while holding up a sufficient precision in the geometry description (see [2]). Moreover, it simplifies the shape derivatives as it provides an implicit description for the moving interfaces. The sub‐meshing technique makes it possible to keep existing strategies from homogeneous structures and to transform them on a discontinuous material using enriched shape functions provided by the standard extended finite element method (see [3]). Shape sensitivities are evaluated on the sub‐elements and extrapolated to the interface introducing pseudo nodes. The sensitivity information of the stress field among these pseudo nodes can be used in the framework of stress minimisation as well as for a side condition in a volume minimisation setup.