幂强化材料和超弹性材料组合球体中孔穴的动态生成

在简单加载条件下,研究幂强化材料和超弹性材料组合球体中的动态孔穴生成和增长问题.首先在有限变形动力学的框架下建立了相应的非线性数学模型,得到了应力的表达式,利用变量变换的方法求得了外加载荷和孔穴半径之间的一个精确的微分关系式.证明了当突加载荷超过其临界值时,球体内部有孔穴的突然生成,并随时间呈现非线性的周期振动.通过数值计算,分析了材料参数和球体的半径比对孔穴生成和增长的影响,并与相应的静态结果进行了比较.结果发现,惯性力的影响降低孔穴生成的临界载荷,而且材料的塑性对孔穴生成和增长有明显的影响.

DYNAMICAL FORMATION AND GROWTH OF CAVITY IN A SPHERE COMPOSED OF POWER HARDENING MATERIAL AND HYPER-ELASTIC MATERIAL

The bifurcation problem of dynamical formation and growth of cavity in a sphere composed of a power hardening material and a hyper-elastic material is discussed in this paper. A mathematical model is first presented based on the dynamical theory of finite deformations. An exact differential relation between the void radius and surface load is obtained by using the variable transformation method, and the stress expressions after the void formation are also given. One can see that there exists void formation in the sphere when the load is larger than its critical value and the evolvement of void radius with time displays a kind of non-linearly periodic vibration. The influence of the material parameters on the void formation and growth is considered by numerical computation and the results are compared with those for static analysis. Results show that the inertia force will reduce the critical value of load and that the effect of the plasticity of material on the formation and growth of cavity is evident.