不可压缩组合球体的空穴和分叉

Cavitation and Bifurcation in an Incompressible Composite Sphere

利用有限变形弹塑性理论和超弹性理论,研究了组合线性强化弹塑性-超弹性球体在径向拉伸死载荷作用下的空穴生成问题。确定了外载荷与空穴半径的函数关系,给出了空穴形成时应力的分布,讨论了材料硬化参数对外载荷和应力分布的影响。结果表明:空穴半径是以某有限值突然出现的,且存在着上界和下限;拉伸死载荷随着空穴半径的增大先减小再增大;径向应力在空穴处为零而环向应力则在空穴处形成应力集中,其实正是这种应力集中,导致了空穴的出现。本文的研究结论可以为橡胶材料的增韧技术提供一定的理论参考依据。

Based of the finite deformation elastic-plastic theory and the hyperelastic theory, formation of a cavity in a solid sphere composed of incompressible elastic linear-hardening and hyperelastic materials subjected to a radial tensile dead load on the boundary was examined. The relationship between dead load and radius of the cavity was determined and the stress distributions were also obtained. At the same time, the influences of material＇s hardening parameter on the dead load and the stress distribution were given. The results indicated that the cavity took place abruptly as a finite radius and it had a upper bound and a lower limit, that the dead load decreased firstly, then increased with the increment of the radius of cavitation, and that on the surface of the formed cavitation the radial stress was zero while the circumferential stress was infinity. In fact, this kind of stress concentration lead to the emergence of the cavitation. The results here may be helpful as a theoretical reference in the plasticizing technology of rubber materials.