Calculus of Variations and Geometric Measure Theory
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A. Braides - M. Solci

Asymptotic analysis of Lennard-Jones systems beyond the nearest-neighbour setting: a one-dimensional prototypical case

created by braidesa on 04 Jul 2014
modified on 19 Aug 2016


Published Paper

Inserted: 4 jul 2014
Last Updated: 19 aug 2016

Journal: Math. Mech. Solids
Volume: 21
Pages: 915-930
Year: 2016
Doi: 10.1177/1081286514544780


We consider a one-dimensional system of Lennard-Jones nearest and next-to-nearest neighbour interactions. It is known that if a monotone parameterization is assumed then the limit of such a system can be interpreted as a Griffith fracture energy with an increasing condition on the jumps. In view of possible applications to a higher-dimensional setting, where an analogous parameterization seems not always reasonable, we remove the monotonicity assumption and describe the limit as a Griffith fracture energy where the increasing condition on the jumps is removed and is substituted by an energy that accounts for changes in orientation (`creases'). In addition, fracture may be generated by `macroscopic' or `microscopic' cracks.

Keywords: Gamma-convergence, fracture mechanics, Lennard-Jones potentials, discrete-to-continuum, atomistic systems


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