Atomic to continuum passage for nanotubes. Part I: a discrete Saint-Venant principle
نویسندگان
چکیده
We consider general nanotubes of atoms in R3 where each atom interacts with all others through a two-body potential. When there are no exterior forces, a particular family of nanotubes is the set of perfect nanotubes at the equilibrium. When exterior forces are applied on the nanotube, we compare the nanotube to nanotubes of the previous family. This quantitative comparison is formulated in our main result as a Saint-Venant principle. This estimate can be derived for a large class of potentials (including Lennard-Jones potential), when the perfect nanotubes at the equilibrium are stable. The approach is designed to be applicable to general nanotubes that can be for instance carbon nanotubes or DNA. In a second paper [22] (part II), we derive from our Saint-Venant principle, a macroscopic mechanical model for general nanotubes. AMS Classification: 35J15, 49M25, 65L70, 74A60.
منابع مشابه
Atomic to continuum passage for nanotubes. Part II: error estimates
We consider deformations in R3 of an infinite general nanotube of atoms where each atom interacts with all the other through a two-body potential. We compute the effect of an external force applied to the nanotube. At the equilibrium, the positions of the atoms satisfy an Euler-Lagrange equation. For large classes of potentials (including Lennard-Jones potential) and under suitable stability as...
متن کاملCrack analysis of an orthotropic circular bars reinforced by a magnetic coating under Saint-Venant torsion
This paper presents an analytical solution for an orthotropic circular cross section bar with a magnetic coating weakened by multiple arbitrary oriented cracks under Saint-Venant torsion by means of the distributed dislocation technique. At first, the solution of the orthotropic bar with a magnetic coating weakened by a Volterra-type screw dislocation is achieved with the aid of the finite Four...
متن کاملA reciprocity theorem in linear gradient elasticity and the corresponding Saint-Venant principle
In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be use...
متن کاملInelastic Continuum Modeling of Carbon Nanotube,s Behavior Using Finite Element Method
This paper describes a continuum model for analyzing the inelastic behavior of a single walled carbon nanotube (SWCNT) in different loading conditions. Because of limitations in using molecular dynamics (and other atomic methods) to model the failure load of the SWCNT, continuum mechanics methods are considered in this paper. Based on some experimental and theoretical results, an elasto-plastic...
متن کاملFinite-Volume Solvers for a Multilayer Saint-Venant System
We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Sai...
متن کامل