基于界面重构的三维弹塑性MMALE计算方法

A MMALE Method Based on Interface Reconstruction for Three-dimensional Elastic-Plastic Multi-material Flow

针对弹塑性流体特点,通过弹塑性混合网格封闭模型、三维大变形网格上界面重构以及保物理特性弹塑性量重映方法等技术,给出一种适应弹塑性流体的三维MMALE(multi-material arbitrary Lagragian-Eulerian)算法。首先,在混合网格封闭模型方面,针对传统体模量加权模型应用于弹塑性流体导致的压力不平衡问题,通过引入松弛机制和自适应松弛系数,实现压力平衡,同时该封闭模型无须迭代,避免了在迭代过程可能遇到的不收敛问题,提升了健壮性;在界面重构方面,针对三维多面体网格由于变形及三维特殊性导致的守恒性问题,通过引入逐级表面三角化算法,实现了适应三维任意多面体网格上的严格守恒的界面重构。在弹塑性量重映方面,针对偏应力按分量重映后导致的张量性质破坏,应变能不守恒的问题,通过引入对应力张量不变量的重映,实现重映后应力不破坏屈服准则,并保持应变能的守恒性。最后,采用MMALE算法对典型算例进行数值模拟,验证了其正确性和处理大变形问题的健壮性。

The MMALE(multi-material Arbitrary Lagrangian Eulerian method)is an effective method for the simulation of multi-material flow with large deformation.Traditional MMALE methods are mainly used in pure fluids and focus on two-dimensional problems.In this paper,we propose a three-dimensional MMALE algorithm for elastic-plastic fluids by developing three key technologies:a closure model for elastic-plastic flow,an interface reconstruction method adapted to three-dimensional grids with large deformation,and a physical property preserving remapping method for elastic-plastic quantities.Firstly,to solve the pressure imbalance problem caused by elastic-plastic fluids using traditional bulk modulus weighted closure models,a relaxation mechanism is introduced in our new closure model to achieve the balance of the pressure.At the same time,this model does not require iterations,avoiding the difficulties of non convergence that may be encountered during the iteration process;Secondly,in order to address the conservation issues caused by distorted three-dimensional polyhedral grids,a step-by-step surface triangulation algorithm is introduced to preserve the conservation during the interface reconstruction process.Thirdly,in the aspect of the remapping of elastic-plastic quantities,aiming at the problem that the tensor property is destroyed and the strain energy is not conserved after the deviator stress is remapped component by component,the remapping of invariants of the stress tensor is introduced to preserve the tensor property and maintain the conservation of the strain energy.Finally,the MMALE method is used to simulate several typical examples,and its correctness and robustness are verified.