A scaled boundary multiscale approach to crack propagation

Abstract

In this work, we fuse the scaled boundary finite element method (SBFEM) on balanced hybrid quadtree-polygon (QT) meshes with the extended multiscale finite element method (EMsFEM) to accelerate crack propagation simulations. This scaled boundary multiscale approach to crack propagation 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 domain, 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 computational 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 domains. 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 negatively 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.