In the paper, the plastic deformation of heterogeneous materials is analyzed by direct numerical simulation based on the theory of an elastic-plastic orthotropic Cosserat continuum, with the plasticity condition taking into account both the shear and rotational mode of irreversible deformation. With the assumption of a block structure of a material with elastic blocks interacting through compliant plastic interlayers, this condition imposes constraints on the shear components of the asymmetric stress tensor, which characterize shear, and on the couple stresses, which irreversibly change the curvature characteristics of the deformed state of the continuum upon reaching critical values. The equations of translational and rotational motion together with the governing equations of the model are formulated as a variational inequality, which correctly describes both the state of elastic-plastic deformation under applied load and the state of elastic unloading. The numerical implementation of the mathematical model is performed using a parallel computing algorithm and an original software for cluster multiprocessor systems. The developed approach is applied to solve the problem of compressing a rectangular brick-patterned blocky rock mass by a rough nondeformable plate rotating with constant acceleration. The effect of the yield stress of the compliant interlayers on the stress-strain state of the rock mass in shear and bending is studied. The field of plastic energy dissipation in the rock mass is analyzed along with the fields of displacements, stresses, couple stresses, and rotation angle of structural elements. The obtained results can help to validate the hypothesis about the predominant effect of curvature on plastic strain localization at the mesolevel in microstructural materials.

中文翻译：

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基于正交各向异性 Cosserat 连续体理论的塑性变形建模

本文基于弹塑性正交各向异性Cosserat连续体理论，通过直接数值模拟分析了异质材料的塑性变形，塑性条件同时考虑了不可逆变形的剪切和旋转模式。假设材料具有块状结构，弹性块通过柔顺的塑料夹层相互作用，该条件对表征剪切的非对称应力张量的剪切分量和耦合应力施加了约束，这不可逆地改变了材料的曲率特性。连续体在达到临界值时的变形状态。平移和旋转运动方程与模型的控制方程一起被公式化为变分不等式，它正确地描述了外加载荷作用下的弹塑性变形状态和弹性卸载状态。数学模型的数值实现是使用并行计算算法和用于集群多处理器系统的原始软件进行的。应用所开发的方法解决了通过以恒定加速度旋转的粗糙的不可变形板压缩矩形砖状块状岩体的问题。研究了柔性夹层的屈服应力对岩体剪切和弯曲应力应变状态的影响。分析了岩体中的塑性能量耗散场以及结构单元的位移场、应力场、耦合应力场和旋转角场。