In this paper, we present a method to achieve smooth nodal stresses in the XFEM application.
This method was developed by borrowing the ideas from the 'twice interpolating approximations'
(TFEM) by Zheng et al (2011). The salient feature of the method is to introduce an
'average' gradient into the construction of the approximation, resulting in improved solution
accuracy, both in the vicinity of the crack tip and in the far eld. Due to the higher-order polynomial
basis provided by the interpolants, the new approximation enhances the smoothness of
the solution without requiring an increased number of degrees of freedom. This is particularly
advantageous for low-order elements and in fracture mechanics. Since the new approach adopts
the same mesh discretization, i.e. simplex meshes, it can be easily extended to various problems
and is easily implemented. We also discuss the increased bandwidth which is a major drawback
of the present method. Numerical tests show that the new method is as robust as the XFEM,
considering precision, model size and post-processing time. By comparing the results from the
present method with the XFEM for crack propagation in homogeneous material, we conclude
that for two-dimensional problems, the proposed method tends to be an e fficient alternative to
the classical XFEM.
