Strain Energy Density of Generalized Stoney Model with Cylindrical Coordinate
Abstract: The relation of strain-stress is an important aspect of understanding mechanical property of materials. 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 substrate, 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.
文章引用: 李 佳 , 史俊杰 , 刘辉昭 (2015) 柱坐标下推广的Stoney模型的应变能密度。 力学研究， 4， 71-75. doi: 10.12677/IJM.2015.44009
Stoney, G.G. (1909) The Tension of Metallic Films Deposited by Electrolysis. Proceedings of the Royal Society of London, 82, 172-175.
 李佳, 史俊杰, 吴洁君, 刘辉召, 齐浩然. GaN-蓝宝石异质厚膜体系界面应力特性研究[J]. 力学研究, 2014(3): 55-64.
Floro, J.A., Lucadamo, G.A., Chason, E., Freund, L.B., Sinclair, M., Twesten, R.D. and Hwang, R.Q. (1998) SiGe Island Shape Transitions Induced by Elastic Repulsion. Physical Review Letters, 80, 4717.
 杨海波, 曹建国, 李洪波编著. 弹性与塑性力学简明交城[M]. 北京: 清华大学出版社, 2011.