柱坐标下推广的Stoney模型的应变能密度.pdfVIP

International Journal of Mechanics Research 力学研究, 2015, 4(4), 71-75 Published Online December 2015 in Hans. /journal/ijm /10.12677/ijm.2015.44009 Strain Energy Density of Generalized Stoney Model with Cylindrical Coordinate 1* 2 1 Jia Li , Junjie Shi , Huizhao Liu 1 School of Science, Hebei University of Technology, Tianjin 2 State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, Research Center for Wide-Gap Semiconductors, School of Physics, Peking University, Beijing th th th Received: Oct. 30 , 2015; accepted: Nov. 17 , 2015; published: Nov. 20 , 2015 Copyright © 2015 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract The relation of strain-stress is an important aspect of understanding mechanical property of ma- terials. According to it, we can further obtain the strain energy function of materials, and a series of other mechanical properties. The Stoney model is based on the relation of strain-stress of sub- strate, and the strain energy function is first obtained, and then the relation between stress in film and curvature is achieved. At the present case, we generalize the Stoney model, considering the strain and stress of z direction, and as well as shear strain related to z direction, and we obtain the strain energy function at any point with cylindrical coordinate. In addition, we obtain the integral expression of strain energy of system by considering of the in-plane uniform mismatch strain of the film. Keywords Strain and Stress, Mechanics, Stoney Model, Shear Strain, Strai