Nonlinear Elasticity from Atomistic Mechanics

Abstract

We present sharp convergence results for the Cauchy--Born approximation of general classical atomistic interactions, for both static and dynamic problems, for small data.

revised preprint with some minor error corrected and an extended introduction

References in corpus (4)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Energy transport by acoustic modes of harmonic lattices
• Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice
• A Note on Linear Elliptic Systems on ${\mathbb{R}}^d$

Cited by in corpus (4)

• Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods
• Gamma-expansion for a 1D Confined Lennard-Jones model with point defect
• Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model
• A priori and a posteriori $W^{1,\infty }$ error analysis of a QC method for complex lattices