This work addresses the determination of yield surfaces for geometrically exact elastoplastic rods. Use is made of a formulation where the rod is subjected to an uniform strain field along its arc length, thereby reducing the elastoplastic problem of the full rod to just its cross-section. By integrating the plastic work and the stresses over the rod’s cross-section, one then obtains discrete points of the yield surface in terms of stress resultants. Eventually, Lamé curves in their most general form are fitted to the discrete points by an appropriate optimisation method. The resulting continuous yield surfaces are examined for their scalability with respect to cross-section dimensions and also compared with existing analytical forms of yield surfaces.

这项工作致力于确定几何精确的弹塑性棒的屈服面。使用这样的配方，其中杆沿其弧长方向受到均匀的应变场，从而将整个杆的弹塑性问题减小到仅其横截面。通过将塑性功和杆横截面上的应力进行积分，就可以根据应力合力获得屈服面的离散点。最终，通过适当的优化方法将最一般形式的Lamé曲线拟合到离散点。检查所得连续屈服面在横截面尺寸方面的可扩展性，并与屈服面的现有分析形式进行比较。