用于板料成形反向模拟的特殊应力更新算法

提出了一种改进的反向模拟法，以最终构型为研究对象，采用Euler坐标系，基于虚功原理 获得有限元列式. 改进的反向模拟法采用了一种基于塑性流动理论的本构方程，可以充分考 虑应变历史对塑性变形的影响. 为了避免流动理论应力更新算法过程中关于未知量\Delta \lambda 的非线性方程的求解，引入等效应力思想，无需Newton-Raphson迭代直 接计算未知量\Delta \lambda . 盒形件的拉深实例中，传统的基于塑性形变本 构方程的反向模拟法和改进的基于塑性流 动本构方程的反向模拟法计算结果，分别与基于增量有限元法的正向数值模拟求解器 LS-DYNA计算结果进行对比. 通过获得的坯料轮廓、成形极限图、等效应变分布、计算效率 等的比较，验证了所提出的基于塑性流动理论本构模型的应力更新算法的有效性.

A NOVAL STRESS INTEGRATION ALGORITHM IN INVERSE ANALYSIS METHOD OF SHEET METAL STAMPING

An improved inverse analysis method is proposed for sheet metal stamping based on the final workpiece in Euler coordinate system. The principle of the virtual work is firstly adopted to obtain the equivalent equations. The constitutive equation in the present method is based on flow theory of plasticity to consider the loading history, while deformation theory of plasticity in the classical inverse analysis method. The plastic multiplier \Delta \lambda is directly obtained with the concept of the equivalent stress in order to avoid numerous iterations in Newton-Raphson scheme \Delta \lambda. The numerical results obtained from the classical and improved inverse analysis methods are compared with those from the incremental forward finite element solver LS-DYNA. It shows that the proposed constitutive equation is effective and reliable with the comparisons of blank configurations, Forming Limited Diagram (FLD), the effective strain distribution and computational efficiency.