An adaptive singular finite element in nonlinear fracture mechanics

In the case of nonlinear fracture mechanics the type of singularity induced by the crack tip is commonly not known. This results in a poor approximation of the near crack tip fields in a finite element setting and induces so called spurious—or residual—discrete material forces in the vicinity of the crack tip. Thus the numerical calculation of the crack driving material force in nonlinear fracture is often not that precise as in linear elasticity where we can use special crack tip elements and/or path independency. To overcome this problem we propose an adaptive singular element, which adapts automatically to the type of singularity. The adaption is based on an optimisation procedure using a variational principle.