Shape-sensitivity-based evaluation of the stress intensity factors at the nanoscale by means of quantized fracture mechanics

An approach based upon the concept of shape sensitivity is presented for numerically evaluating the quantized fracture mechanics (QFM) stress intensity factors (SIFs) in the absence of an analytical expression for the linear elastic fracture mechanics SIFs. This approach is general and can be employed in conjunction with any numerical techniques such as finite element or boundary element methods to evaluate the QFM SIFs at the nanoscale for many fracture problems in engineering practice. Some numerical examples involving benchmark problems in fracture mechanics are reported to demonstrate the validity and accuracy of the proposed technique when it is coupled with a numerical method like the symmetric-Galerkin boundary element method.