理想弹塑性压力敏感性材料中球形孔洞的动态扩展研究

Dynamic expansion of the spherical cavity in the elastic perfectly-plastic pressure sensitive material

通过椭圆形的屈服方程和自相似假设,结合Hopkins三区模型,研究了理想弹塑性压力敏感性材料中球形孔洞的动态扩展问题,得到了塑性区场量的非线性控制微分方程组。通过弹性区的应力场以及弹塑性边界的塑性屈服条件,给出了塑性区的初值,并应用打靶法给出了问题的数值解。结果表明:与幂硬化材料中的应力场变化不同,理想弹塑性压力敏感性材料中,应力场的变化较小,且基本不受参数孔洞膨胀速度m和压力敏感性参数α1、α2的影响;随到孔边距离的减小,应变明显增大,同时相对密度稍有增大。

The pressure-sensitive material(such as rock) is one kind of materials widely used in the engineering fields,so it owns important engineering meaning to study its mechanical characteristics.The dynamic expansion problem of the spherical cavity in the elastic perfectly-plastic pressure sensitive material is studied based on the elliptic-equation yield criterion,self-similar hypothesis and Hopkins three regions model.The nonlinear differential equations to solve the dynamic expansion problem in the plastic region are firstly derived according to the research of the basic equations.Then the initial values of the plastic field are also gained by the research of the stress fields in the elastic region and the plastic yield condition in the intersection between the elastic and plastic region.Finally,numerical solutions of this problem are obtained by the shooting method.The results obtained indicate that the parameters of the pressure-sensitive material have a small effect on the stress fields while have a great effect on the density and strain fields.