Issue 29

A. Infuso et alii, Frattura ed Integrità Strutturale, 29 (2014) 302-312; DOI: 10.3221/IGF-ESIS.29.26 302 Focussed on: Computational Mechanics and Mechanics of Materials in Italy Flaw-tolerance of nonlocal discrete systems and interpretation according to network theory A. Infuso Politecnico di Torino, Department of Structural, Geotechnical and Building Engineering, Corso Duca degli Abruzzi 24, 10129 Torino, Italy andrea.infuso@polito.it M. Paggi IMT Institute for Advanced Studies Lucca, P.zza San Francesco 19, 55100 Lucca, Italy marco.paggi@imtlucca.it A BSTRACT . Discrete systems are modeled as a network of nodes (particles, molecules, or atoms) linked by nonlinear springs to simulate the action of van der Waals forces. Such systems are nonlocal if links connecting non-adjacent nodes are introduced. For their topological characterization, a nonlocality index (NLI) inspired by network theory is proposed. The mechanical response of 1D and 2D nonlocal discrete systems is predicted according to finite element (FE) simulations based on a nonlinear spring element for large displacements implemented in the FE programme FEAP. Uniaxial force-displacement responses of intact and defective systems (with links or nodes removed) are numerically simulated. Strain localization phenomena, size-scale effects and the ability to tolerate defects are investigated by varying the degree of nonlocality. K EYWORDS . Nonlocality; Discrete systems; MDFEM; Large displacements; Network theory. I NTRODUCTION onlocal continuum theories based on gradient models, integral formulations or fractional calculus have been widely explored in mechanics to describe long-range interactions (see e.g. [1-10], among others). At the same time, discrete systems composed of particles or molecules have been proposed in the physics community to analyze the behaviour of materials at the nano or micro scales. Lattice beam models [11], albeit suffering from mesh dependency due to the local nature of the bonds/links, have been extensively used to simulate the meso-scale behavior of concrete. Efforts accounting for nonlocal effects, such as the three-dimensional Born model [12], have been proposed to study the distribution of broken bonds within a homogeneous discrete mechanical system. With the progress in computer technology, wide tridimensional discrete systems can nowadays be modelled by molecular dynamics (MD), accounting for nonlinear interatomic potential laws and nonlocal interactions among the discrete molecules. Attempts to couple MD with FEM have been explored in [13], with the intent to perform multi-scale analyses where discrete systems are connected to continuum finite elements. In the present study, the ability of nonlocal molecular systems to tolerate flaws is investigated. To this aim, a nonlinear spring element for large displacements whose constitutive relation is ruled by van der Waals forces is implemented in the N