非均匀温度场中组合热超弹性球体的动态孔穴生成

Dynamical Formation of Cavity for Composed Thermal Hyperelastic Spheres in Non-Uniform Temperature Fields

在有限变形动力学的框架下,研究了在非均匀温度场中组合热超弹性球体,在表面均布拉伸死载荷作用下的动态孔穴的生成和增长问题.首先建立了相应的非线性数学模型,利用换元积分方法求得了孔穴半径与外加载荷之间的一个精确的微分关系,并进行了数值计算,得到了不同温度下球体中孔穴生成时的临界载荷和分叉曲线.考察了参数对孔穴生成与增长的影响,并与相应的静态结果进行了比较.结果表明孔穴是以一个有限的半径突然出现的,且随时间的演变孔穴半径呈现周期性的非线性振动;当温度升高,临界值降低,同时在相同的条件下动态临界载荷低于静态临界载荷.

Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials are discussed under the case of a non-uniform temperature field and 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 are considered and compared with that 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.