Nonlocal analysis of edge-cracked nanobeams under Mode I and Mixed-Mode (I + II) static loading

In the present paper, the behavior of an edge-cracked nanobeam under both Mode I and Mixed-Mode (I + II) static bending loading is analyzed by using the stress-driven nonlocal model (SDM), being the SDM applied for the first time in the case of Mixed-Mode loading. More precisely, the cracked nanobeam is modeled by using a modification of the classical cracked-beam theory, consisting in dividing the beam into two beam segments connected through a massless elastic rotational spring located at the cracked cross section. The bending stiffness of the cracked cross section is computed by exploiting: the Griffith energy criterion and the conventional linear elastic fracture mechanics. Cracks under both Mode I and Mixed-Mode (I + II) loading are considered. Finally, an edge-cracked cantilever nanobeam subjected to a transversal point load at the free end is analyzed. The static deflection is calculated and discussed for different values of relative crack depth, crack location, and crack orientation.