基于自然单元法的薄壁空心铝型材挤压成形数值模拟研究

The extrusion processes of thin-walled aluminum hollow profile is usually accompanied by complex large deformations such as welding and forming. Numerical simulations of these processes with traditional methods of finite element or finite volume are difficult, as the former has the problem of mesh distortion and inefficiency in simulating welding process, while the latter is inefficient in tracking free material surface. The recently developed natural element method has significant advantages in analyzing large deformations and tracking free material surface, and therefore has great potential in solving the above-mentioned difficulties. Based on the natural element method, this project aims at developing numerical simulation theory and method of aluminum extrusion processes, which will be further used to examine the forming mechanisms of the aluminum hollow profile extrusions. Specifically, we will firstly develop the coupled thermal-mechanical model of aluminum extrusion process by incorporating the natural element method with the rigid-viscoplastic theory.Boundary-tracking method for the workpiece will be developed based on weighted three-dimensional Delaunay tetrahedron algorithm, and the contact/detachment criteria and dynamic adjustment methods for the workpiece and die in the extrusion process will be established. The self-collision detection and welding judgment methods and the corresponding treatment methods for the workpiece will be introduced. Adaptive analysis method, including the algorithm of adding and deleting nodes adaptively, and adaptive boundary points setting method will be established to improve the simulation accuracy, and GPU data stream parallel computing acceleration method will be developed to improve computation efficiency.

薄壁空心铝型材挤压成形过程中材料会发生分流、焊合、成形等复杂大变形，采用传统的有限元方法或有限体积法对其进行数值模拟非常困难，因为前者存在网格畸变和焊合过程难以模拟等问题，而后者则在材料自由表面追踪方面存在显著不足。近年来发展起来的自然单元法在分析复杂大变形和追踪变形体边界流动方面具有突出优势，非常适用于上述研究。本项目以自然单元法为基础，发展铝型材挤压成形数值模拟理论和方法，探索薄壁铝型材挤压成形机理。具体地，项目将自然单元法和刚粘塑性理论相结合，建立铝型材挤压成形热力耦合分析理论模型；发展基于加权三维限定Delaunay四面体剖分方法的变形体边界面追踪方法，并建立焊合过程中金属的自接触和焊合处理方法，和成形过程中变形体与模具的接触处理方法；发展自适应分析方法，并设计自适应加密、删除节点算法和边界节点加密方法，以提高模拟精度；发展基于GPU的数据流并行计算方法，以提高模拟的计算效率。

采用传统的有限元方法或有限体积法对铝合金挤压等金属塑性成形大变形进行数值模拟存在困难，有限元法存在网格畸变等问题，而有限体积法在材料自由表面追踪方面存在显著不足。自然单元法兼具无网格法和有限元法的优点，在分析复杂大变形和追踪变形体边界流动方面具有突出优势，项目将自然单元法应用于铝合金挤压等金属塑性成形数值模拟，并在以下几个方面进行了深入研究：①自然单元的理论研究，包括求解域的离散、自然邻近点搜索、形函数构造、积分方案算法等；②将自然单元法和刚/粘塑性理论相结合，建立了刚/粘塑性自然单元法，开展了热力耦合分析的相关算法研究；③研究了自然单元法在数值分析铝型材挤压等金属塑性成形中所涉及的关键问题，主要有变形体与模具的接触、脱离的判断和修正处理方法，数值模拟中初始速度场的获取方法，解决了数值仿真中出现的体积闭锁问题；④发展自适应分析方法，并设计自适应加密节点算法和边界节点加密方法，以提高模拟精度；⑤提出了一种基于精确Delaunay三角化网格半边数据结构的自然邻近点快速搜索算法，在一定程度上提高了自然单元法处理弹性问题的计算效率；提出了基于K近邻的K值自适应的局部自然邻近点快速搜索算法，该算法对于弹性问题和塑性问题均具有很强的适应性；研究了基于CPU的并行计算方法，提高了程序的计算效率。⑥利用开发的程序研究了铝合金挤压工艺，研究了模具结构和工艺对铝合金内部物理场量的影响规律，揭示铝合金挤压成形金属流动规律。