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.

Asymptotic analysis of microscopic impenetrability constraints for atomistic systems

GELLI, MARIA STELLA
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.
2016
Braides, A; Gelli, MARIA STELLA
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/825759
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