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Mohr-Coulomb准则由于角点问题的存在导致其在数值计算时收敛困难,首先阐述了其角点问题的实质是主应力随罗德角的变化而不光滑导致的,然后给出了主应力空间法的理论基础,最后基于Koiter法则在主应力空间将Mohr-Coulomb准则的多屈服面表达为其等价的互补模型,并进一步用Fischer-Burmeister互补函数进行描述,从而使得牛顿算法可以顺利地进行求解。所提出的算法解决了Mohr-Coulomb准则中的角点问题,避免了常规方法的试算过程,提高了Mohr-Coulomb准则的精度。算例验证了该方法的有效性和可靠性。
The Mohr-Coulomb criterion is difficult to converge in numerical calculation due to the existence of corner points. Firstly, the essence of the corner problem is that the principal stress is not smoothed with the change of the Rhodes angle. Then, the principal stress space method Finally, based on the Koiter’s law, the multi-yield surface of Mohr-Coulomb criterion is expressed as its complementary model in principal stress space and further described by Fischer-Burmeister complementary function, so that Newton’s algorithm can be successfully solved . The proposed algorithm solves the corner problem in the Mohr-Coulomb criterion, avoids the trial calculation of the conventional method and improves the accuracy of the Mohr-Coulomb criterion. The example shows the validity and reliability of the method.