An analytical solution for thermal shock analysis of multiwall carbon nanotubes

Thermo-elastic stress field in shock-induced multiwall carbon nanotubes (MWCNTs) is analyzed using an analytical method. The linear model of van der Waals forces is applied between two adjacent tubes in the MWCNTs with finite length to simulate the force between layers. The presented method is based on a dynamic continuum model of 3D elasticity solution in cylindrical shells. In addition, to create realistic physical properties, the temperature dependence of material properties is considered for the problem. All governing equations are transferred to frequency domain using Laplace transform technique to solve analytically the time dependent governing equations. The results in Laplace domain are transferred to time domain using an inverse Laplace transformation method. The accuracy of solution is verified by comparison with those obtained from literature. The results are obtained for two types of MWCNTs with 4 and 13 layers. To access a proper design of MWCNTs under thermal shock, the effects of their sizes on dynamic behaviors of thermal stresses are studied in details. It is found that thermal shock has a significant effect on disturbance of thermo-elastic stress filed in time domain, which is studied for various types of MWCNTs in this paper.