屈服面角点奇异性的非平滑处理对塑性应变的影响

Effect on plastic strain through the non-smoothness management of corner singularity

Mohr-Coulomb屈服面的边界角点奇异性问题,使得屈服面在这些部位的微分出现不连续现象,给数值分析带来了诸多困难,针对此问题,平滑及非平滑处理方法得以应用,其中,非平滑处理方法中的回代求导法和塑性应变增量求和法等因易于实现而应用较多。这些方法精度的研究多相对于某些典型算例而进行的,而对于塑性应变的发展遵循何规律,非平滑处理方法对塑性应变产生何影响,如何评价这种影响效应等等问题尚未在理论上被深入研究。为此,在传统塑性位势理论的框架内对塑性剪应变的发展规律,以及通过非平滑处理后塑性剪应变的发展规律进行了理论研究。研究发现,在角点奇异性屈服面的非平滑处理方法中,最终推导出的塑性剪应变出现不连续现象。通过对这一现象进行的理论研究和定量分析,结果表明:非平滑处理对塑性应变存在影响效应(即不连续效应),故对于具体问题,应具体分析这些方法的影响效应,具体评估其计算结果的可靠性和对相应问题的适用性,以便正确选择所采用的处理方法。

The discontinuities of the differential of yield surface to stress components at the comers are caused by the comer singularity of Molar-Coulomb yield surface, resulting in many problems in the numerical simulation. With regard to these problems, a lot of treating methods are introduced including the smoothness and the non-smoothness methods in the previous studies, in which the non-smoothness disposal methods have been widely applied for their simple implementation. And the studies on their precision have been carried out in many classical cases. But it is not clear that what the rules of the plastic strain are and what the effect of these methods on the plastic strain is. Furthermore, deep researches have not been conducted on how to evaluate the effect quantitatively. So firstly, the flow rules of the plastic shear strain are studied in the frame of the conventional plastic potential theory. Then, the discontinuity phenomenon of the plastic shear strain is discovered in the researches on the rules of the plastic shear strain in which the non-smoothness management is applied. The results of the analysis of this phenomenon indicate that the discontinuity of the plastic shear strain can not be neglected. So, the precision of these different methods should be concretely analyzed in consideration of different cases.