Mechanical Behaviour of Multiple Cracked Nanobeams: A Novel Analytical Model

The aim of the present paper is to propose a novel nonlocal analytical model to investigate the mechanical behaviour of a multiple cracked nanobeam subjected to bending load. Such a model is a reformulation of that proposed by some of the present authors for a single cracked nanobeam, and exploits the Stress Driven nonlocal Model within the Euler-Bernoulli beam theory. According to such a novel formulation, the nanobeam is split in correspondence of each of the n cracks, thus obtaining n+1 segments connected to each other by means of massless elastic rotational springs. The stiffness of each spring is computed by using firstly the Griffith's energy criterion and then the conventional Linear Elastic Fracture Mechanics, where the stress intensity factor is computed through a finite element modelling. The proposed model is employed to simulate a bending test performed on a cantilever microbeam containing two edge-cracks, and a parametric study is performed by varying the depths of the cracks, their reciprocal distance and the position of the first crack in order to explore how such parameters influence the mechanical response of the above microbeam.