Nonlinear equations of deformation of atomic lattices

Abstract

This paper presents vector, scalar and variational forms of motion/equilibrium equations of atomic lattices. An automated method is suggested for constructing the matrices and vectors of equations based on summing the corresponding local matrices and vectors of atomic pairs. The exact expression for the tangential stiffness matrix of an atomic pair is obtained where both the change in the segment length of a straight line connecting atoms in this pair and rotation of the segment are taken into account.