Issue 29

A. Infuso et alii, Frattura ed Integrità Strutturale, 29 (2014) 302-312; DOI: 10.3221/IGF-ESIS.29.26 308 (a) (b) Figure 8 : Global force vs. global displacement curves. (a) The effect of NLI for a system with a size h  4  l 0 . (b) The effect of the size h of the system with NLI=2. For a given degree of nonlocality, e.g., NLI=2, the effect of the size of the system can be explored by increasing the number of nodes at a distance l 0 for each pair (see Fig. 8(b)). As a trend, the peak force does not change, whereas the post-peak response becomes more and more brittle by increasing h . Monodimensional model with defects Let us consider a system with 5 nodes ( h  4  l 0 ) and with a broken link (see Fig. 9(a)). This can be the case in nanoscopic systems when there is an atomic vacancy or a weakened interatomic potential due to dislocations. The problem is solved numerically under displacement control and a very complex behaviour of the various springs is observed. To comment on that, it is useful to analyze the force-nodal distance curve of each spring, Fig. 9(b). All the springs in series (1, 3, 4) are initially in the initial branch of the van der Waals forces and all of them experience an elastic unloading (see the direction of the arrows in Fig. 9(b)). Springs 5, 6 and 7 used to model long-range interactions are all in the softening branch of the van der Waals force diagram. The spring 7 experiences an increasing in the corresponding load level due to the shortening of springs 3 and 4. On the other hand, 5 and 6 increase their elongation monotonically in time. The global response, shown in Fig. 10(a) presents softening due to the heavy damage induced by the removal of a local link. However, the defect can be tolerated due to the nonlocality and the load-carrying capacity of the system is an increasing function of NLI, see Fig. 10(a). By increasing the system size and removing only the second spring in all the cases, the force is an increasing function of h as shown in Fig. 10(b), as the same was observed in case of a defect-free system. (a) (b) Figure 9 : (a) Geometry of the 5 nodes system without the link no. 2. (b) Force-displacement diagram of the springs.