Issue 29

A. Infuso et alii, Frattura ed Integrità Strutturale, 29 (2014) 302-312; DOI: 10.3221/IGF-ESIS.29.26 311 provides an intermediate response. This trend is in line with the fact that the removal of two adjacent nodes is particularly critical and induces a significant number of removed links. The effect of NLI is particularly important. The system with NLI=1 is initially compressed, due to the fact that the nodes are initially at a distance slightly smaller than the equilibrium one given by the L-J potential. By increasing NLI, further links in a tension state are introduced and reduce this initial compressive stress state. Although the nodes removal has a higher impact on the systems characterized by higher nonlocality indices since a larger number of links is removed, the force is an increasing function of NLI, thus showing that nonlocality has a very important role for flaw-tolerance. Figure 14 : Comparison of the force-displacement curves varying NLI, depending on the type of defect. C ONCLUSIONS aking into consideration nonbonded interactions between nodes according to the L-J generalized potential, the influence of nonlocality on the mechanical response of discrete systems has been investigated. In the monodimensional case, we have observed a complex behaviour of the links depending on the nonlocality index NLI. In the case of a link absent or removed, a phenomenon analogous to strain localization observed in continuum systems has been evidenced. Results on bi-dimensional systems have also shown the important role exerted by the nonlocality on the load carrying capacity of the system and its ability to tolerate defects or vacancies. The proposed approach and its further extension to 3D can be applied to predict strength and stiffness of discrete systems as, e.g., 2D graphene layers of carbon-carbon bonds, or nanotubes, represented by a 3D network of carbon atoms. Moreover, a constitutive law based on L-J potential is definitely useful to study problems where interactions between two different materials are governed by nonbonded forces. This is for example the case of an interphase boundary interaction between collagen and graphene. Future developments regarding the implementation of bonded interactions, including not only stretching energy, but also bending and torsion energy contributions to describe physical links between atoms or molecules, are envisaged. ACKNOWLEDGEMENTS he financial support of the Italian Ministry of Education, University and Research to the Project FIRB 2010 Future in Research “Structural mechanics models for renewable energy applications” (RBFR107AKG) is gratefully acknowledged. R EFERENCES [1] Aifantis, E.C. ,On the gradient approach – Relation to Eringen’s nonlocal theory, Int. J. Eng. Sci., 49 (2001) 1367- T T