A nonlocal linear elastic fracture formulation is presented based on a discrete layer approach and an interface model to study cracked nanobeams. The formulation uses the stress-driven nonlocal theory of elasticity to account for the size-dependency in the constitutive equations, and the Bernoulli-Euler beam theory to define the kinematic field. Two fundamental mode I and mode II fracture nanospecimens with applications in Engineering Science are studied to reveal principal characteristics of the linear elastic fracture of beams at nanoscale. The domains are discretized both through the transverse and longitudinal directions and the field variables are derived by solving systems of the nonlocal equilibrium equations subjected to the variationally consistent and constitutive boundary and continuity conditions. The energy release rates of the fracture nanospecimens are calculated both from the global energy consideration and from the localized fields at the tip of the crack, i.e. the cohesive forces and the displacement jumps. The results are shown to be the same, proving the capability of the interface model to predict localized fields at the crack tip which are important for the cohesive fracture problems. It is found that the nanospecimens with higher nonlocality have higher fracture resistance and load bearing capacity due to higher energy absorptions and lower energy release rates. The crack propagation in the nanospecimens are also studied and load-displacement curves are presented. The nonlocality considerably increases the stiffness of the initial linear response of the nanospecimens. The fracture model is also able to capture the non-linear post-peak response and the unstable crack propagation, the snap-back instability, which is more intense for nanospecimens with higher nonlocality.

提出了一种基于离散层方法和界面模型的非局部线性弹性断裂配方，以研究破裂的纳米束。该公式使用应力驱动的非局部弹性理论来解释本构方程中的尺寸依赖性，并使用Bernoulli-Euler梁理论来定义运动场。研究了在工程科学中应用的两种基本的I型和II型断裂纳米样品，以揭示纳米级梁的线性弹性断裂的主要特征。通过横向和纵向离散域，并通过求解变分一致且本构边界和连续性条件下的非局部平衡方程组来求解场变量。断裂纳米标本的能量释放速率是根据整体能量考虑和裂纹尖端的局部场（即内聚力和位移跳跃）来计算的。结果表明是相同的，证明了界面模型能够预测裂纹尖端的局部场，这对于内聚断裂问题很重要。发现由于较高的能量吸收和较低的能量释放率，具有较高非局部性的纳米样品具有较高的抗断裂性和承载能力。还研究了裂纹在纳米试样中的扩展，并给出了载荷-位移曲线。非局部性大大增加了纳米样品的初始线性响应的刚度。