High order X-FEM and levelsets for complex microstructures: Uncoupling geometry and approximation

In this contribution, a strategy is proposed for uncoupling geometrical description and approximation with the X-FEM. The strategy is based on an uniform coarse mesh that defines a high order approximation of the mechanical fields and an adapted mesh that defines the geometrical features by means of levelsets. The connection between the geometry and the approximation is obtained by sharing the quadtree trees of the two meshes. Numerical examples involving level-set based parts, convergence studies, mechanical computations and numerical homogenization show good promise for this approach.

► Propose a high-order X-FEM approximation that can be easily extended to 3D.
► Uncouple geometry and approximation using two mesh octree approach.
► Use Nitsche’s method to obtain optimal convergence rates for material interfaces.
► Exponential convergence rates can be obtained for both free surfaces or material interfaces.