Mohr-Coulomb准则的弹塑性积分方法

Elastoplastic Integral Algorithm for Mohr-Coulomb Criterion

基于Koiter法则,提出一种适用于Mohr-Coulomb非光滑本构模型的弹塑性积分方法;阐述Mohr-Coulomb准则角点问题产生的原因,采用经典的Kuhn-Tucker互补条件判断可能活跃的屈服面,将Kuhn-Tucker互补方程作为一类特殊的变分不等式,使用投影收缩算法进行求解,并进一步通过迭代确定实际活跃的屈服面;基于主应力特征方程,在主应力空间中计算屈服函数对应力分量的偏导数,同时在一般应力空间中执行应力返回。结果表明,所提出的算法解决了Mohr-Coulomb准则的角点问题,消除了光滑角点带来的误差,既避免了Mohr-Coulomb屈服函数在一般应力空间中角点处的数值奇异性,又不需要进行主应力空间法中所需的应力变换。

Based on Koiter’s rule,an elastoplastic integral method for Mohr-Coulomb non-smooth constitutive model was proposed.The cause of Mohr-Coulomb criterion corner problem was described,and the classical Kuhn-Tucker complementary condition was then used to judge the possible active yield surface.By taking Kuhn-Tucker complementary equation as a special case of variational inequality,the problem was solved by using projection contraction algorithm,and the actual active yield surface was further determined iteratively.On the basis of principal stress characteristic equation,the partial derivative of yield function corresponding to the stress component was calculated in principal stress space,and the stress return was performed in general stress space.The results show that the corner problem of Mohr-Coulomb criterion is solved by using the proposed algorithm,and the error caused by corner round-off is eliminated.Numerical singularity of Mohr-Coulomb yield function in general stress space and stress transformation required in principal stress space method are avoided simultaneously.