中文摘要：

提出一种新的多步反向模拟法，该方法建立在虚功原理的基础上，为提高计算精度，采用弹塑性材料模型。提出一种适用于多步反向模拟法的本构关系，可以充分考虑弹／塑性变形状态、加载／卸载状况。提出一种“双截面线法”来快速获取中间构型，可以充分考虑塑性变形对构型的影响。提出一种快速接触搜索算法来实现中间构型各个节点在约束滑移面上的移动，采用全局搜索和局部搜索策略相结合的方法，加快搜索速度。理论成果已经在自主开发的板料成形反向模拟软件InvvrStamp／Multi-step模块中实现。在盒形件多步拉深实例中，坯料轮廓、等效应变分布等计算结果与基于ls-dyna的增量法模拟软件Dynaform计算的结果十分吻合，验证了多步反向模拟法相比于一步反向模拟法的优势。

英文摘要：

A novel multi-step inverse analysis method based on .the principle of virtue work is proposed. Elasto-plastic material model is adopted to improve calculation accuracy. In order to fully consider the actual forming condition such as elastic/plastic deformation or loading/unloading, a modified constitutive equation for multi-step inverse analysis method is presented. A new ＂double section curve expanding method＂ is proposed to get initial solutions of intermediate configurations which can take into account of plastic deformation characteristics. A fast and reliable local and global combined searching scheme is used to restrain the moving of corresponding nodes. Above mentioned improvements are implemented in our in-house inverse analysis software InverStamp/Multi-stop module. The presented algorithms are applied to a square cup multistage drawing example. The numerical results compared to ls-dyna based software Dynaform confirm their validity and efficiency.