Buckling simulation of single crystalline Mg nanowaire: eigenvalue and eigenvectors of atomic elastic stiffness at onset of bending

Abstract

In order to reveal the precursor of buckling by the eigenvalue/vectors of the atomic elastic stiffness, Baij = Δσai/Δεj (atomic stress and strain in the Voigt notation), molecular dynamics simulations are performed on a single crystalline Mg nanowire of 5nm×5nm×104nm (infinite bar under periodic boundary) with the three compressive directions of the [0001], [1210] and [1010]. The corner atoms of the nanowires show negative 1st eigenvalue, ηa(1) (the solution of the eigen-equation of {Baij}{Δεj} = ηa{Δεi}), or “unstable” in the initial equilibrium; and the other atoms never become ηa(1) < 0 at the onset of bending. Thus we investigated the distribution of the ηa(1) in each corner and found that the position of the minimum ηa(1) was close to the peak point of the Euler buckling curve. The deformation modes of these unstable corner atoms are also visualized by the maximum principal strain direction calculated by the strain compornent of the corresponding eigenvectors, {Δεi} = {Δεxx,··· ,Δγxy}T.

Keywords

• atomic elastic stiffness
• local instability
• buckling
• nanowire
• hcp metals