Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials

The stress tensor is described as a symmetric tensor in all classical continuum mechanics theories and in most existing statistical mechanics formulations. In this work, we examine the theoretical origins of the symmetry of the stress tensor and identify the assumptions and misinterpretations that lead to its symmetric property. We then make a direct measurement of the stress tensor in molecular dynamics simulations of four different material systems using the physical definition of stress as force per unit area acting on surface elements. Simulation results demonstrate that the stress tensor is asymmetric near dislocation cores, phase boundaries, holes and even in homogeneous material under a shear loading. In addition, the atomic virial stress and Hardy stress formulae are shown to significantly underestimate the stress tensor in regions of stress concentration.

Evaluation of the Surface Tension of Silicon-Gold Binary Liquid Alloy

The gold-catalyzed vapor-liquid-solid (VLS) method is widely used for silicon nanowire (Si NW) fabrication. As the VLS process is influenced by the physical properties of the catalytic silicon-gold (Si-Au) droplet, quantifying the surface tension of the liquid alloy is important to achieve better control of the wire growth. Because the experimental measurement of the surface tension is difficult, it is necessary to obtain reasonable estimates from computational models. In this work, we conducted molecular dynamics simulations with a modified embedded-atom potential developed for the Si-Au binary system, and evaluated the surface tension γ based on the Virial stress expression. The dependence of surface tension γ on the Si fraction χ and temperature T is predicted. The entropy of the liquid-vapor interface was extracted from the slope of the γ-T curve. The Si concentration and stress distributions near the surface are also predicted. Our surface tension evaluation enables theoretical predictions of droplet and nanowire shape, and provides physical inputs for continuum phase field models of VLS growth.

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Stress intensity factor is one of the most significant fracture parameters in linear elastic fracture mechanics (LEFM). Due to its simplicity, many researchers directly employed this concept to explain their results from molecular simulation. However, stress intensity factor defines the amplitude of the singular stress, which is the product of continuum elasticity. Under atomistic systems without the stress singularity, the concept of stress intensity factor must be examined. In addition, the difficulty of studying the stress intensity factor in atomistic systems may be traced back to the ambiguous definition of the local atomistic stress. In this study, the definition of the local virial stress is adopted. Subsequently, through the consideration of K-dominance, the approximated stress intensity factor based on the atomistic stress can be projected within a reasonable region. Moreover, the influence of cutting interatomic bonds to create traction free crack surfaces and the critical stress intensity factor is also discussed.

Damage Mechanics of Carbon Nano Tubes Under Uniaxial Tension

A procedure is proposed for computing the stresses in an armchair Single-Walled Carbon NanoTube (SWCNT) under uniaxial tension. Computation is based on molecular dynamics simulations and the virial stress theorem. The proposed approach is compared with other methods used in the literature for calculating the stresses in CNTs. The loading is applied under two different boundary conditions and different strain rates and the results are compared. It is shown that the method commonly used in the literature for calculating the stresses in CNTs under estimates the ultimate strength by around 35%. It is shown that the value of the displacement increment used to apply the tensile strain is crucial.