Nonlocal stress gradient integral model with discontinuous and symmetrical conditions for size-dependent fracture of centrally-cracked nanobeams

We study the fracture of nanobeams containing central cracks using nonlocal stress gradient integral model (NSGIM) with discontinuous and symmetrical conditions. Compared with the traditional NSGIM, the present model includes some definite integral terms in the constitutive boundary constraints and the newly introduced constitutive continuity conditions. Subsequently, the Mode I and Mode II fracture problems are studied under given uniform loading (or concentrated force) conditions in opposite and same directions. In the numerical simulations, the effects of nonlocal and gradient length scale parameters on normalized energy release rates and works by external loads are investigated in detail.