Cosserat连续介质的Mohr-Coulomb屈服准则及其应用

Cosserat连续介质下的应力、应变张量具有不对称性,经典连续介质的屈服准则无法直接用于Cosserat连续介质. 将应变、应力张量分解为对称和反对称两部分,修正了经典连续介质下三个应力不变量的表达式,建立适用于Cosserat连续介质弹塑性有限元分析的Mohr-Coulomb屈服准则,给出了Cosserat连续介质下von Mises、Tresca和Drucker-Prager屈服准则的表达式. 自然边坡数值算例表明了修正Mohr-Coulomb屈服准则的有效性,验证了Cosserat连续介质理论通过引入材料特征长度可以解决经典连续介质理论分析应变局部化问题时遇到的网格敏感性问题.

Mohr-Coulomb yield criterion for Cosserat continua and its applications

Classical yield criterions cannot be applied directly to Cosserat continua since the strain tensor and stress tensor in Cosserat continua are asymmetric. The strain tensor and stress tensor were decomposed into symmetric and skew-symmetric components, and the formulae of stress invariants were modified for Cosserat continua. Mohr-Coulomb yield criterion for Cosserat continua was established in detail, and the formulae of von Mises, Tresca and Drucker-Prager yield criterions for Cosserat continua were presented as well. Elasto-plastic finite element method based on these yield criterions was addressed. A numerical example on slope stability under gravity shows the superior behavior of the established Mohr-Coulomb yield criterion, and demonstrates that the Cosserat model incorporating an internal length scale can resolve the mesh-dependence that classical continua encounter in the strain localization problem.