A novel analytical approach for simulating the mechanical behavior of multi-cracked nanobeams

This paper presents a novel nonlocal analytical model for simulating the mechanical behaviour of a nanobeam with multiple cracks under bending. The proposed model incorporates the StressDriven Nonlocal Model within the framework of the Euler-Bernoulli beam theory, dividing the nanobeam into n + 1 beam segments at each of the n crack locations. These segments are connected by massless elastic rotational springs, whose stiffness is determined using both the Griffith's energy criterion and Linear Elastic Fracture Mechanics. Firstly, the study focuses on asymmetric double cracks, characterised by different lengths and relative distances, for which Stress Intensity Factors are computed using finite element simulations. Then, the proposed model is validated against experimental data from the literature, specifically data on edge-cracked microbeams composed of NiAl single crystals subjected to bending. Finally, a parametric study is conducted varying crack lengths and distances to evaluate their influence on the mechanical response of the microbeam. The main objective of this research work is to provide valuable insights for the design and analysis of nanoscale structures with multiple cracks, contributing to various engineering applications.