Issue 29

A. Infuso et alii, Frattura ed Integrità Strutturale, 29 (2014) 302-312; DOI: 10.3221/IGF-ESIS.29.26 307 1 and 5 have elongations monotonically increasing during the simulation. The force level of the local spring 1 is much higher than that of the nonlocal spring 5. This is due to the fact the spring 5 is connecting nodes that are at an initial distance twice larger than that of the spring 1. Springs 2 and 6, after an initial positive relative displacement between their connected nodes, then experience a progressive reduction of their elongations with a consequent elastic unloading. Figure 6 : Sketch of the discrete system with 5 nodes by varying NLI. (a) NLI=1; (b) NLI=2; (c) NLI=3. (a) (b) Figure 7 : System with 5 nodes and NLI=2. (a) Spring forces vs. imposed displacement. (b) Spring nodal positions vs. imposed displacement. A similar response takes place for the system with NLI=3. Springs 1, 5 and 6 have an elongation monotonically increasing with time, whereas springs 2 and 6 experience an elastic unloading after an initial increased separation. A comparison between the force-displacement curves of the various systems depending on NLI is shown in Fig. 8(a). The nonlocality increase the peak force observed in case of NLI=1. Moreover, a gain in the capacity of tolerating defects takes place, as we will quantify in the next subsection. The difference between the responses of the systems with NLI=2 and NLI=3 is quite small, in line with the observation that nonlocal interactions are rapidly decaying by increasing the nodal distance, see Fig. 2(b). (b) (c) (a)