The problem of radial symmetric motion for a solid sphere composed of a class of generalized incompressible neo-Hookean materials, subjected to a suddenly applied surface tensile dead load, is examined.The ana...The problem of radial symmetric motion for a solid sphere composed of a class of generalized incompressible neo-Hookean materials, subjected to a suddenly applied surface tensile dead load, is examined.The analytic solutions for this problem and the motion equation of cavity that describes cavity formation and growth with time are obtained. The e?ect of radial perturbation of the materials on cavity formation and its motion is discussed. The plane of the perturbation parameters of the materials is divided into four regions. The existential conditions and qualitative properties of solutions of the motion equation of the cavity are studied in di?erent parameters’ regions in detail. It is proved that the cavity motion with time is a nonlinear periodic vibration. The vibration center is then determined.展开更多
Dynamical formation and growth of compressible thermal-hyperelastic Gent-Thomas cavity in a sphere composed of two inmaterials were discussed under the case of a non-uniform temperature field and the surface dead load...Dynamical formation and growth of compressible thermal-hyperelastic Gent-Thomas cavity in a sphere composed of two inmaterials 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 stiddenly 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.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10272069) and Shanghai Key Project Program.
文摘The problem of radial symmetric motion for a solid sphere composed of a class of generalized incompressible neo-Hookean materials, subjected to a suddenly applied surface tensile dead load, is examined.The analytic solutions for this problem and the motion equation of cavity that describes cavity formation and growth with time are obtained. The e?ect of radial perturbation of the materials on cavity formation and its motion is discussed. The plane of the perturbation parameters of the materials is divided into four regions. The existential conditions and qualitative properties of solutions of the motion equation of the cavity are studied in di?erent parameters’ regions in detail. It is proved that the cavity motion with time is a nonlinear periodic vibration. The vibration center is then determined.
基金Project supported by the National Natural Science Foundation of China (No.10272069)Shanghai Leading Academic Discipline Project (No.Y0103)
文摘Dynamical formation and growth of compressible thermal-hyperelastic Gent-Thomas cavity in a sphere composed of two inmaterials 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 stiddenly 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.
