Flaw-tolerance of nonlocal discrete systems and interpretation according to network theory

Abstract

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.

Computational Modeling of Discrete Mechanical Systems and Complex Networks: Where We are and Where We are Going

“…Discrete systems have been firstly introduced in physics (Fisher and Wiodm, 1969;Noor and Nemeth, 1980;Adhikari et al, 1996;Kornyak, 2009) to simulate materials at the micro-and nano-scales where a continuum description of matter breaks down. The constituents can be atoms or molecules and their interactions are usually modeled by force fields resulting from chemical potentials or weak van der Waals interactions, depending on the type of bonding.…”

“…Therefore, given the elementary constitutive equations describing the link behavior that can be mechanically modeled as non-linear springs and the state variables characterizing the nodes, the basic dynamics of any discrete system can be in principle simulated according to the numerical techniques proper of non-linear mechanics. A non-locality index can also be used to classify and distinguish between different networks, as shown in Infuso and Paggi (2014) to interpret the response of a discrete system upon removal of nodes in different locations. From numerical simulations in Infuso and Paggi (2014), we observed that the higher the value of the non-locality index, the higher the total force supported by the network, for the same type of node removal.…”

“…A non-locality index can also be used to classify and distinguish between different networks, as shown in Infuso and Paggi (2014) to interpret the response of a discrete system upon removal of nodes in different locations. From numerical simulations in Infuso and Paggi (2014), we observed that the higher the value of the non-locality index, the higher the total force supported by the network, for the same type of node removal.…”