VARIATIONAL APPROACH FOR A NEW DIRECT-INTEGRATION FORM OF THE VIRTUAL CRACK EXTENSION METHOD

A new direct-integration technique for the virtual crack extension method which employs variational theory in the finite element formulation is presented. The formulation proposed here not only provides accurate results but also is simpler and more general than the earlier forms. Moreover, this method can be extended to drive higher order derivatives of the energy release rate, e.g., the rates of the energy release rate for mixed-mode fracture. With Betti's theorem and the mutual energy concept, a simple but effective uncoupling technique for mixed-mode stress intensity factors is also possible. Combined with the higher order derivatives of the energy release rate, this uncoupling technique can be used to derive the first derivatives of the stress intensity factors which in turn can be employed for better prediction of crack stability and rate of propagation.