A unified finite element method for determining weight functions in two and three dimensions

A variational principle is introduced for determining singular fields in finite bodies with unbounded strain energy. A specialized form of this variational principle is employed to determine the Bueckner-Rice weight functions in two and three dimensions. The cracked body considered is finite, linear elastic and homogeneous but arbitrary anisotropy is permitted. It contains an arbitrary configuration of planar cracks with continuously turning crack fronts. A finite element implementation of the variational principle is given and this leads to a unified approach in the numerical computations of weight functions for all three fracture modes. The finite element method presented is simple and yet accurate and it can be incorporated into standard finite element programs. Numerical examples are given for two-dimensional crack geometries in isotropic bodies to illustrate the versatility and accuracy of the method.