Developments in Extended Finite Element Methods for Extraction of Strain Energy Release Rates and Computational Nanomechanics for

In this dissertation, developments in computational mechanics are presented in two parts. In the first part, a new analytical approach, within the extended finite element (XFEM) framework, is proposed to compute Strain Energy Release Rates (SERRs) directly from Irwin’s integral. Crack tip enrichment functions in XFEM allow for evaluation of integral quantities in closed form (for some crack configurations studied) and therefore results in an accurate and efficient method. The effects of high order enrichments, mesh refinement and the integration limits of Irwin’s integral are examined in benchmark numerical examples. The results indicate that high order enrichment functions have significant effect on the convergence, in particular when the integral limits are finite. When the integral limits tend to zero, simpler SERR expressions are obtained and high order terms vanish. Nonetheless, these terms contribute indirectly via coefficients of first order terms. The analytical formulation is then extended to cracks in arbitrary orientations. Several benchmark examples are investigated including off-center cracks, inclined cracks and crack growth problems. On all these problems, the method is shown to work well, giving accurate results. Moreover, due to its analytical nature, no special postprocessing is required whic