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.

Asymptotic analysis of Lennard-Jones systems beyond the nearest-neighbour setting: a one-dimensional prototypical case / Braides, A; Solci, Margherita. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - 21:8(2016), pp. 915-930. [10.1177/1081286514544780]

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

SOLCI, Margherita
2016-01-01

Abstract

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.
2016
Asymptotic analysis of Lennard-Jones systems beyond the nearest-neighbour setting: a one-dimensional prototypical case / Braides, A; Solci, Margherita. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - 21:8(2016), pp. 915-930. [10.1177/1081286514544780]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/56824
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