Communications in Mathematical Sciences
Volume 13 (2015)
A discrete to continuum analysis of dislocations in nanowire heterostructures
Pages: 1105 – 1133
Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a corresponding variational discrete model with quadratic pairwise atomic interaction energy. By employing the notion of Gamma-convergence and a geometric rigidity estimate, we perform a discrete to continuum limit and a dimension reduction to a one-dimensional system. Moreover, we compare a defect-free model and models with dislocations at the interface and show that the latter are energetically convenient if the thickness of the wire is sufficiently large.
nonlinear elasticity, discrete to continuum, dimension reduction, rod theory, geometric rigidity, non-interpenetration, Gamma-convergence, crystals, dislocations, heterostructures
2010 Mathematics Subject Classification
49J45, 70G75, 74B20, 74K10, 74N05