Abstract Computational models are investigated to analyze plane strain pure bending of rectangular cross sectional curved microbeams in elastic and partially plastic states. A generalization of classical von-mises deformation theory of plasticity is adopted to include size effect, by considering intrinsic material length scale parameter, in the modeling. Assuming linear and power-law hardening model, the governing nonlinear equation in elastic-plastic zones are discretized by generalized differential quadrature (GDQ) method and are solved by direct iteration approach. The numerical calculations of proposed model are validated with published literature. Semi-analytical solution is obtained from the special case of curved microbeam with elastic-rigid plastic constitutive model and linear hardening law. The influences of initial curvature and size effect on yielding initiations at the inner and outer surfaces of microstructure are evaluated. Also, distributions of stress components along the microbeam thickness are studied, for different values of the couple moments, at elastic limits and beyond.

中文翻译：

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用于弯曲梁状 MEMS 器件纯弯曲分析的微塑性模型

摘要 研究了计算模型来分析弹性和部分塑性状态下矩形截面弯曲微梁的平面应变纯弯曲。通过在建模中考虑固有的材料长度尺度参数，采用经典的 von-mises 塑性变形理论的推广来包括尺寸效应。假设线性和幂律硬化模型，弹塑性区的控制非线性方程通过广义微分正交（GDQ）方法离散，并通过直接迭代方法求解。所提出模型的数值计算得到了已发表文献的验证。利用弹-刚塑性本构模型和线性硬化规律，从弯曲微梁的特殊情况得到半解析解。评估了初始曲率和尺寸效应对微观结构内外表面屈服起爆的影响。此外，还研究了应力分量沿微梁厚度的分布，对于不同的偶矩值，在弹性极限和超出弹性极限。