Abstract

An analysis of the properties of the constitutive equations of the theory of plasticity for porous media using Green’s yield criterion is carried out. It is shown that this criterion is one of the possible yield criteria for materials with plastic properties depending on the type of stress state, with the only difference being that the coefficients depend on the porosity parameter. Therefore, the yield criterion can be represented in an appropriate generalized form using a parameter of the form of the stress state, which is the ratio of the hydrostatic stress component to the effective von Mises stress, called in the literature the stress triaxiality. A semi-analytical solution to the problem of a space with a cylindrical hole under plane strain conditions is obtained. The stress distributions corresponding to the obtained solution is compared with the stress distributions in a similar problem for a solid, which plastic properties are invariant to the type of the stress state. The effect of porosity on the stress distribution and the size of the plastic region is investigated.

中文翻译：

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平面变形下多孔介质中圆孔附近的应力场

摘要

利用格林的屈服准则对多孔介质塑性理论的本构方程的性质进行了分析。结果表明，该标准是具有塑性特性的材料（取决于应力状态类型）的可能屈服标准之一，唯一的区别是系数取决于孔隙率参数。因此，屈服准则可以使用应力状态形式的参数以适当的广义形式表示，该参数是静水应力分量与有效冯·米塞斯应力之比，在文献中称为应力三轴性。获得了在平面应变条件下具有圆柱孔的空间问题的半解析解。将与获得的溶液相对应的应力分布与类似问题的固体中的应力分布进行比较，该问题的塑性性质对于应力状态的类型是不变的。研究了孔隙率对应力分布和塑性区域尺寸的影响。