A finite element (FE) formulation is presented for a direct approach to model elastoplastic deformation in slender bodies using the special Cosserat rod theory. The direct theory has additional plastic strain and hardening variables, which are functions of just the rod's arc‐length, to account for plastic deformation of the rod. Furthermore, the theory assumes the existence of an effective yield function in terms of stress resultants, that is, force and moment in the cross‐section and cross‐section averaged hardening parameters. Accordingly, one does not have to resort to the three‐dimensional theory of elastoplasticity during any step of the finite element formulation. A return map algorithm is presented in order to update the plastic variables, stress resultants and also to obtain the consistent elastoplastic moduli of the rod. The presented FE formulation is used to study snap‐through buckling in a semicircular arch subjected to an in‐plane transverse load at its midsection. The effect of various elastoplastic parameters as well as pretwisting of the arch on its load–displacement curve are presented.

中文翻译：

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直接用于特殊Cosserat杆的弹性塑性的有限元公式

提出了一种有限元（FE）公式，用于直接使用特殊的Cosserat杆理论对细长物体中的弹塑性变形进行建模。直接理论具有附加的塑性应变和硬化变量，它们仅是杆的弧长的函数，以说明杆的塑性变形。此外，该理论假设存在有效的屈服函数，即应力合力，即横截面和横截面的平均硬化参数中的力和弯矩。因此，在有限元公式化的任何步骤中都不必诉诸于弹塑性的三维理论。为了更新塑性变量，应力结果并获得杆的一致弹塑性模量，提出了一种返回图算法。提出的有限元公式用于研究在半圆形拱的中部承受平面内横向载荷的快速弯折。提出了各种弹塑性参数以及拱的预绕对其荷载-位移曲线的影响。