Bi-Helmholtz kernel based stress-driven nonlocal integral model with discontinuity for size-dependent fracture analysis of edge-cracked nanobeam

Abstract

Mathematical formulation is proposed to deal with average bi-Helmholtz kernel (BHK) based stress-driven nonlocal integral model (SDNIM) with discontinuity, which is converted into equivalent differential form with constitutive constraints. Based on average BHK-SDNIM with discontinuity, mathematical model for size-dependent fracture behavior of mode I and II cracks is established for edge-cracked nanobeam. For different load conditions, the analytical bending deflections are deduced firstly, and the corresponding external works and energy release rates can be calculated explicitly. Numerical study shows that energy release rates decrease with the increase of nonlocal parameter which explains the superior fracture performance of nano-materials.