中文摘要：

传统板料成形反向模拟法的本构关系是建立在塑性形变理论的基础上,无法考虑变形历史的影响。提出一种新型有效的多步反向模拟法,采用弹塑性材料模型提高计算精度;引入DKT12薄壳单元考虑类似模具圆角处的弯曲—反弯曲效应等应变历史的影响。提出一种基于塑性流动理论的本构方程,可以快速准确地处理弹/塑性变形及加载/卸载状况,提高了应力计算精度。在应力应变更新计算中引入等效应力思想,避免了大量迭代计算,保证数值计算稳定性的同时,提高了计算效率。研究的理论成果已成功实现在自主开发的板料成形反向模拟法软件InverStamp/Multi-step模块。在S形轨道拉深实例中,通过显式有限元程序LS-DYNA与两种反向模拟法计算结果的比较,证明采用新型本构关系的多步反向模拟可以更为准确地预测成形零件的厚度分布。

英文摘要：

Because of the shortcoming of plastic deformation theory of the traditional inverse finite element method of sheet metal forming：No consideration of the effect of deformation history,a novel multi-step inverse finite element method based on the principle of virtue work is proposed.Elasto-plastic material model is adopted to improve calculation accuracy.DKT12 shell element is introduced to consider the effect of deformation history such as bending-unbending around die entrance.In order to improve the stress calculation,a novel constitutive equation based on plastic flow theory is proposed,which can well reflect the actual forming condition such as elastic/plastic deformation or loading/unloading condition.The notion of the equivalent stress is adopted for stress and strain updating,which in turn can avoid numerous iterations to ensure the numerical stability and maintain the calculation efficiency at the same time.Above mentioned improvements are implemented in our in-house inverse analysis software InverStamp/Multi-step module.The presented algorithms are applied to S-rail deep drawing example.The numerical results compared with explicit dynamic solver LS-DYNA confirm its validity in prediction of the thickness distribution of formed part.