On the effect of interactions beyond nearest neighbours on non-convex lattice systems

DOI10.1007/s00526-017-1129-5zbMath1362.74008OpenAlexW2574614690MaRDI QIDQ526947

Mariapia Palombaro, Giuliano Lazzaroni, Roberto Alicandro

Publication date: 15 May 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: http://sro.sussex.ac.uk/id/eprint/66948/1/A-L-P-2016-surface-scaling_FINAL-Accepted.pdf

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Crystalline structure (74E15) Energy minimization in equilibrium problems in solid mechanics (74G65) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in equilibrium problems of solid mechanics (74Q05)

Related Items (11)

A variational model for dislocations at semi-coherent interfaces ⋮ Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces ⋮ Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours ⋮ A compactness and structure result for a discrete multi-well problem with \(\mathrm{SO}(n)\) symmetry in arbitrary dimension ⋮ A note on locking materials and gradient polyconvexity ⋮ Microscopic Validation of a Variational Model of Epitaxially Strained Crystalline Films ⋮ On the effect of interactions beyond nearest neighbours on non-convex lattice systems ⋮ Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals ⋮ Variational Analysis of a Two-Dimensional Frustrated Spin System: Emergence and Rigidity of Chirality Transitions ⋮ Derivation of Linear Elasticity for a General Class of Atomistic Energies ⋮ Optimal regularity estimates for general nonlinear parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A discrete to continuum analysis of dislocations in nanowire heterostructures
• Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires
• On the effect of interactions beyond nearest neighbours on non-convex lattice systems
• A proof of crystallization in two dimensions
• Piecewise rigidity
• An introduction to \(\Gamma\)-convergence
• Linear elastic chain with a hyper-pre-stress.
• On Lennard-Jones systems with finite range interactions and their asymptotic analysis
• From molecular models to continuum mechanics
• Asymptotic analysis of microscopic impenetrability constraints for atomistic systems
• On the derivation of linear elasticity from atomistic models
• A derivation of linear elastic energies from pair-interaction atomistic systems
• Effective cohesive behavior of layers of interatomic planes
• BOUNDARY LAYER ENERGIES FOR NONCONVEX DISCRETE SYSTEMS
• A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models
• A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• A Γ‐convergence result for the two‐gradient theory of phase transitions
• Asymptotic analysis of Lennard-Jones systems beyond the nearest-neighbour setting: A one-dimensional prototypical case
• Surface energies emerging in a microscopic, two-dimensional two-well problem
• SURFACE ENERGIES IN NONCONVEX DISCRETE SYSTEMS
• Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance

This page was built for publication: On the effect of interactions beyond nearest neighbours on non-convex lattice systems