Simulation of bar with a straightness defect crossing a cylindrical guidance tool using the hybrid elerian lagrangian (HEL) formalism

This data set presents the hybrid eulerian-lagrangian (HEL) formalism in finite element modelling. It consists of coupling steady state (eulerian) and time depending (lagrangian) phenomena, that occur in material flow, using Arlequin method. Each type of phenomenon is represented by an appropriate mesh. In this dataset it is exposed how HEL can be useful for long and flat product fabrication. Contact areas with tools have steady state aspect. Outside, structural instabilities inducing geometrical defects are time depending. In this context HEL offers the opportunity to model material drawing in contact with three or two dimensional eulerian elements and structural behavior outside with lagrangian (improved with ALE formalism) shell or beam elements. The animation in the dataset presents a representative two-dimensional case of circular cross-sectional steel bar passing through guidance tool. Inside contact with tool two dimensional mesh with quadrilateral linear elements is used (20x3 elements). Structural behavior (straightness) is characterized by mesh with quadratic beam elements (30 elements). At eulerian mesh extremities, incoming and outgoing velocities (identical and equal to 1000mm/s) are imposed at inlet and outlet of contact area (eulerian mesh) which makes lagrangian mesh transported from upstream to downstream. Contact is supposed frictionless and replaced by blocking vertical velocities in the upper and lower surfaces in the eulerian mesh. Upstream and downstream extremeties of the beam are fixed (vertical velocity and displacement are blocked to stabilize the structure). A case with incoming defect is presented and bar supposed not stretched. Time increment is constant in the simulation and taken 0.5ms.

本数据集阐述了有限元建模中的混合欧拉-拉格朗日（Hybrid Eulerian-Lagrangian, HEL）形式化方法。该数据集采用阿尔坎（Arlequin）耦合方法，将材料流动中出现的稳态（欧拉）现象与随时间演化的拉格朗日现象进行耦合，两类现象各自通过适配的网格进行表征。本数据集阐释了HEL方法在长条形扁平制品制造中的应用价值：与加工工具的接触区域呈现稳态特征，而接触区域外引发几何缺陷的结构不稳定性则随时间演化。在此场景下，HEL方法可实现两类建模：一是通过三维或二维欧拉单元对接触状态下的材料拉拔过程进行建模，二是采用经任意拉格朗日-欧拉（Arbitrary Lagrangian-Eulerian, ALE）形式化方法改进的拉格朗日壳单元或梁单元对接触区域外的结构行为进行建模。数据集中的动画展示了一个典型的二维案例：圆形截面钢筋通过导向加工工具的过程。在与工具接触的区域内，采用由20×3个四边形线性单元构成的二维网格；表征结构平直度行为的网格则由30个二次梁单元组成。在欧拉网格的两端，即接触区域（欧拉网格）的入口与出口处，分别施加大小一致的入流与出流速度（均为1000mm/s），使拉格朗日网格从上游向下游移动。假设接触为无摩擦状态，通过约束欧拉网格上下表面的竖向速度来等效替代接触边界条件。梁单元的上游与下游端点被固定（约束竖向速度与位移以稳定结构）。此外还展示了带初始缺陷的案例，且假设钢筋未发生拉伸变形。仿真中的时间步长为恒定值0.5ms。