In the paper, inelastic strain localization in homogeneous specimens and mesovolumes of a polycrystalline material is modeled based on the asymmetric theory of an elastoplastic Cosserat continuum in a two-dimensional formulation for plane strain. It is assumed that rotational deformation in loaded materials occurs due to the development of localized plastic deformation as well as bending and torsion of the material lattice at the micro- and nanoscale levels. For this reason, the parameters of the micropolar model are considered as functions of inelastic strain for each local mesovolume of the continuum. It is shown that the observed parabolic hardening can be attributed to a large extent to the development of rotational deformation modes, bending and torsion, and appearance of couple stresses in the loaded material. The modeling results indicate that if rotational deformation is stopped in the loaded material, its accommodation capacity decreases, the local and macroscopic inelastic strains sharply increase, leading to a much more rapid formation of fracture structures. Conversely, the formation of meso- and nanoscale substructures with high lattice curvature in materials promotes the activation of rotational deformation modes, reduction of localized strains, and relaxation of stress concentrators.

中文翻译：

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在非对称 Cosserat 理论框架下考虑局部晶格曲率的中尺度局部非弹性变形建模

在本文中，基于弹塑性 Cosserat 连续体的非对称理论，在平面应变的二维公式中，对均质试样和多晶材料的介观体积中的非弹性应变局部化进行了建模。假设加载材料的旋转变形是由于局部塑性变形的发展以及材料晶格在微米和纳米级的弯曲和扭转而发生的。出于这个原因，微极模型的参数被认为是连续体的每个局部微体积的非弹性应变的函数。结果表明，观察到的抛物线硬化在很大程度上归因于旋转变形模式的发展、弯曲和扭转以及加载材料中出现的耦合应力。建模结果表明，如果加载材料停止旋转变形，其容纳能力下降，局部和宏观非弹性应变急剧增加，导致断裂结构的形成速度更快。相反，材料中具有高晶格曲率的介观和纳米级子结构的形成促进了旋转变形模式的激活、局部应变的减少和应力集中器的松弛。