In this work, we fuse the scaled boundary finite element method (SBFEM) on balanced hy- brid quadtree-polygon (QT) meshes with the extended multiscale finite element method (EMsFEM) to accelerate crack propagation simulations. This scaled boundary multiscale approach to crack prop-…
In this work, we fuse the scaled boundary finite element method (SBFEM) on balanced hy- brid quadtree-polygon (QT) meshes with the extended multiscale finite element method (EMsFEM) to accelerate crack propagation simulations. This scaled boundary multiscale approach to crack prop- agation employs SBFEM in a fully resolved region immediately surrounding the crack tip and coarse elements, i.e., EMsFEM unit cells, in the remaining domain. As the crack propagates across the do- main, unit cells within the immediate crack path are resolved. Once the crack completely transitions a resolved unit cell it is replaced by two newly constructed, coarse unit cells. This approach limits com- putational effort to the crack tip region, primarily replacing the fine mesh on the domain by a coarse one, on which the governing equations are solved. Early results indicate that this method results in a reduction of required degrees of freedom (DOFs) by at least an order of magnitude for simple do- mains. Further techniques, unique to the SBFEM, are exploited to enrich the crack tip element and further reduce the amount of refinement necessary about the crack tip. The latter traditionally neg- atively affects the QT mesh due to the balancing operation. Via fusion of these two techniques, the amount of DOFs during simulations of crack propagation remains tractable.