We propose mixed finite element methods for Cosserat materials that use suitable quadrature rules to eliminate the Cauchy and coupled stress variables locally. The reduced system consists of only the displacement and rotation variables. Four variants are proposed for which we show stability and convergence using a priori estimates. Numerical experiments verify the theoretical findings and higher order convergence is observed in some variables.

翻译：本文针对Cosserat材料提出了混合有限元方法，通过采用适当的数值积分规则在局部消除Cauchy应力与耦合应力变量。简化后的系统仅包含位移与旋转变量。我们提出了四种变体方法，并利用先验估计证明了其稳定性与收敛性。数值实验验证了理论结果，并在部分变量中观测到了高阶收敛现象。