Abstract
The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected to 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. An exact differential relation between the cavity radius and the tensile land was obtained. 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gent A N, Lindley, P B. Internal rupture of bonded rubber cylinders in tension[J].Proc R Soc London, 1959, A249(2):195–205.
Ball J M. Discontinuous equilibrium solutions and cavitations in nonlinear elasticity[J].Phil Trans R Soc London, Ser A, 1982,306(3):557–610.
Horgan C O, Polignone D A. Cavitation in nonlinearly elastic solids: A review[J].Appl Mech Rev, 1995,48(3):471–485.
REN Jiu-sheng, CHENG Chang-jun. Cavitated bifurcation for incompressible hyperelastic material [J].Applied Mathematics and Mechanics (English Edition), 2002,23(8):881–888.
REN Jiu-sheng, CHENG Chang-jun, ZHU Zheng-you. Cavity formation at the center of a sphere composed of two compressible hyper-elastic materials[J].Applied Mathematics and Mechanics (English Edition), 2003,24(9):1009–1016.
Chou-Wang M-S, Horgan C O. Cavitation in nonlinear elastodynamic for neo-Hookean materials [J].Internat J of Engrng Sci, 1989,27(8):967–973.
Knowles J K. Large amplitude oscillations of a tube of incompressible elastic material[J].Quart Appl Math, 1960,18(1):71–77.
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.
Calderer C. The dynamical behavior of nonlinear elastic spherical shells[J].J of Elasticity, 1983,13(1):17–47.
REN Jiu-sheng, CHENG Chang-jun. Dynamical formation of cavity in transversely isotropic hyperelastic spheres[J].Acta Mechanica Sinica, 2003,19(4):320–323.
REN Jiu-sheng, CHENG Chang-jun. Dynamical formation of cavity in hyper-elastic materials[J].Acta Mechanica Solida Sinca, 2002,15(3):208–216.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Contributed by CHENG Chang-jun
Foundation items: the National Natural Science Foundation of China (10272069); the Municipal Key Subject Programs of Shanghai
Biographies: REN Jiu-sheng (1970≈)
Rights and permissions
About this article
Cite this article
jiu-sheng, R., Chang-jun, C. Dynamical formation of cavity in a composed hyper-elastic sphere. Appl Math Mech 25, 1220–1227 (2004). https://doi.org/10.1007/BF02438277
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02438277
Key words
- composed incompressible hyper-elastic material
- finite deformation dynamics
- cavity formation
- nonlinear periodic oscillation