A partition of unity boundary element method for fracture and fatigue analysis

The Boundary Element Method (BEM) has become established as a technique well-suited to the modelling of problems containing cracks. If two opposite and equal tractions are applied on the crack faces then two sets of the same equation are included leading to a singular system. Solutions to this problem include the Method of Subregions where the body is split into two regions with the interface region lying along the crack surface. Then, by enforcing equilibrium of tractions and compatability of displacements a solution can be sought [1]. The Dual Boundary Element Method (DBEM) [2] solves the degenerancy by making use of both the displacement integral equation and the traction integral equation which provide two independent equations for collocation along the crack surface. This removes the need for a multi-domain formulation but places some restrictions on the types of element that can be implemented. Further work has been carried out, though, that allows the method to be used with both continuous and discontinuous elements