Dynamical Formation of Cavity in a Composed Hyper-Elastic Sphere
-
摘要: 根据有限变形动力学理论，研究了一个不可压超弹性材料组合球体在突加表面均布拉伸载荷作用下空穴的动态生成问题．当外加载荷超过其临界值时，除一个平凡解外，还有一个包含着球体内部生成的空穴的分叉解；证明空穴随时间的演化是周期性的非线性振动；同时给出了空穴生成时的临界载荷值、空穴振动的相图、振幅及近似的周期．
-
关键词:
- 组合不可压超弹性材料 /
- 有限变形动力学 /
- 空穴的动态生成 /
- 非线性周期振动
Abstract: The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed. -
[1] Gent A N,Lindley P B.Internal rupture of bonded rubber cylinders in tension[J].Proc Roy Soc London,1959,A249(2):195—205. [2] Ball J M.Discontinuous equilibrium solutions and cavitations in nonlinear elasticity[J].Phil Trans R Soc London,Ser A,1982,306(3):557—610. doi: 10.1098/rsta.1982.0095 [3] Horgan C O,Polignone D A.Cavitation in nonlinearly elastic solids: A review[J].Appl Mech Rev,1995,48(3): 471—485. doi: 10.1115/1.3005108 [4] 任九生，程昌钧.不可压超弹性材料中的空穴分叉[J].应用数学和力学，2002，23(8)：783—789. [5] 任九生，程昌钧，朱正佑.可压超弹性材料组合球体中心的空穴生成[J].应用数学和力学，2003,24(9):892—898. [6] Chou-Wang M-S, Horgan C O. Cavitation in nonlinear elastodynamic for neo-Hookean materials[J].Internat J Engrng Sci,1989,27(8):967—973. doi: 10.1016/0020-7225(89)90037-2 [7] Knowles J K. Large amplitude oscillations of a tube of incompressible elastic material[J].Quart Appl Math,1960,18(1):71—77. [8] Guo Z H, Solecki R. Free and forced finite amplitude oscillations of an elastic thick-walled hollow sphere made of incompressible material[J].Arch Mech Stos,1963,15(3):427—433. [9] Calderer C. The dynamical behavior of nonlinear elastic spherical shells[J].J Elasticity,1983,13(1):17—47. doi: 10.1007/BF00041312 [10] REN Jiu-Sheng, CHENG Chang-Jun. Dynamical formation of cavity in transversely isotropic hyperelastic spheres[J].Acta Mechanica Sinica,2003,19(4):320—323. doi: 10.1007/BF02487808 [11] REN Jiu-Sheng, CHENG Chang-Jun. Dynamical formation of cavity in hyper-elastic materials[J].Acta Mechanica Solida Sinca，2002,15(3):208—216. [12] Chalton D.T., Yang J. A review of methods to characterize rubber elastic behavior for use in finite element analysis[J].Rubber Chemistry and Technology,1994,67(3):481—503. doi: 10.5254/1.3538686 -
计量
- 文章访问数: 2644
- HTML全文浏览量: 152
- PDF下载量: 675
- 被引次数: 0
下载:
渝公网安备50010802005915号