We analyze systems of atomistic interactions on a triangular lattice allowing for fracture under a geometric condition on the triangles corresponding to a microscopic impenetrability constraint. Such systems can be thought as a computational simulation of materials undergoing brittle fracture. We show that in the small-deformation regime such approximation can be validated analytically in the framework of variational models of fracture. Conversely, in a finite-deformation regime various pathologies show that the continuum approximation of such a system differs from the usual variational representations of fracture and either needs new types of formulations on the continuum, or a proper interpretation of the atomistic constraints limiting their range and adapting them to a dynamical framework. (C) 2016 Elsevier Ltd. All rights reserved.

Braides, A., Gelli, M.s. (2016). Asymptotic analysis of microscopic impenetrability constraints for atomistic systems. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 96, 235-251 [10.1016/j.jmps.2016.07.016].

Asymptotic analysis of microscopic impenetrability constraints for atomistic systems

Braides A.;
2016-01-01

Abstract

We analyze systems of atomistic interactions on a triangular lattice allowing for fracture under a geometric condition on the triangles corresponding to a microscopic impenetrability constraint. Such systems can be thought as a computational simulation of materials undergoing brittle fracture. We show that in the small-deformation regime such approximation can be validated analytically in the framework of variational models of fracture. Conversely, in a finite-deformation regime various pathologies show that the continuum approximation of such a system differs from the usual variational representations of fracture and either needs new types of formulations on the continuum, or a proper interpretation of the atomistic constraints limiting their range and adapting them to a dynamical framework. (C) 2016 Elsevier Ltd. All rights reserved.
2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Computational mechanics; Variational theory of fracture; Discrete-to-continuum analysis; Gamma-convergence; Lennard-Jones potentials
Braides, A., Gelli, M.s. (2016). Asymptotic analysis of microscopic impenetrability constraints for atomistic systems. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 96, 235-251 [10.1016/j.jmps.2016.07.016].
Braides, A; Gelli, Ms
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/240448
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