Size-Dependent Stress Analysis of Single-Wall Carbon Nanotube Based on Strain Gradient Theory

Abstract

This paper studies stress distribution in a single-walled carbon nanotube (SWCNT) under internal pressure with various chirality. Strain gradient theory is used to capture the size-dependent behavior of the SWCNT. Minimum total potential energy principle is successfully applied to derive the governing differential equation and its associated boundary conditions. Due to complexity of the governing differential equation and boundary conditions, numerical scheme is used to solve the problem. Comparing the results based on strain gradient theory and that of classical elasticity shows a major difference between these two methods. However, a close examination of the results indicates that both theories predict the same trend for variations in the radial displacement along the SWCNT radius. Numerical results also indicate that the proposed model can lead into the classical elasticity model, provided the material length scale parameters are taken to be zero. Additionally, for plane strain condition, the radial displacements predicted by strain gradient theory are lower than those predicted by classical elasticity theory. Moreover, numerical results show that in a SWCNT, the non-dimensional radial and circumferential stresses along the wall thickness of the SWCNT increase as the radius is increased. The opposite behavior is true for non-dimensional high-order stresses.