The Shifted Fracture Method

We propose a new framework for fracture mechanics, based on the idea of an approximate fracture geometry representation combined with approximate interface conditions. Our approach evolves from the shifted interface method, and introduces the concept of an approximate fracture surface composed of the full edges/faces of an underlying grid that are geometrically close to the true fracture geometry. The original interface conditions are then modified on the surrogate fracture geometry, by way of Taylor expansions. The shifted fracture method does not require cut cell computations or complex data structures, since the behavior of the true fracture is mimicked with standard integrals on the approximate fracture surface. Furthermore, the energetics of the true fracture are represented within the accuracy of the underlying polynomial finite element approximation and independently of the grid topology. The computational framework is presented here in its generality and then applied in the specific context of cohesive zone models, with an extensive set of numerical experiments in two and three dimensions.