Calculus of Variations and Geometric Measure Theory

A. Braides - M. Solci

Asymptotic analysis of atomistic systems with long-range interactions

created by braidesa on 14 Jan 2014



Inserted: 14 jan 2014
Last Updated: 14 jan 2014

Year: 2013


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.