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.
Highlights
Nonlocal continuum theories based on gradient models, integral formulations or fractional calculus have been widely explored in mechanics to describe long-range interactions
Discrete systems are modeled as a network of nodes linked by nonlinear springs to simulate the action of van der Waals forces
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
Summary
Nonlocal 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. [1,2,3,4,5,6,7,8,9,10], among others). 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.
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