Abstract
Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials were discussed under the case of a non-uniform temperature field and the surface dead loading. The mathematical model was first presented based on the dynamical theory of finite deformations. An exact differential relation between the void radius and surface load was obtained by using the variable transformation method. By numerical computation, critical loads and cavitation growth curves were obtained for different temperatures. The influence of the temperature and material parameters of the composed sphere on the void formation and growth was considered and compared with those for static analysis. The results show that the cavity occurs suddenly with a finite radius and its evolvement with time displays a non-linear periodic vibration and that the critical load decreases with the increase of temperature and also the dynamical critical load is lower than the static critical load under the same conditions.
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Contributed by CHENG Chang-jun
Project supported by the National Natural Science Foundation of China (No. 10272069) and Shanghai Leading Academic Discipline Project (No.Y0103)
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Cheng, Cj., Mei, B. Dynamical formation of cavity for composed thermal hyperelastic spheres in non-uniform temperature fields. Appl Math Mech 27, 443–452 (2006). https://doi.org/10.1007/s10483-006-0403-z
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DOI: https://doi.org/10.1007/s10483-006-0403-z
Key words
- composed thermal-hyperelastic sphere
- non-uniform temperature field
- dynamical formation and growth of cavity
- nonlinear periodic vibration
- influence of temperature