For the traditional one-step formulations of using shell elements, the computations of the curvature variation and bending stiffness matrix were simplified by omitting the rotational DOFs （degrees of freedom） on the basis of initial flat blank and fully known final configuration. They were highly efficient but not suitable either for the forming processes with non-flat initial configurations or for one-step forward and multistep analyses. Thus, a one-step formulation based on the rotation-free BST （Basic Shell Triangle） element was presented. In this formulation, the penalty method was adopted to deal with contacts in the forming processes.
The miniaturization of products requires the mass production of microparts.The microforming can well meet this requirement.Due to the emergence of decreasing flow stress scale effect in the micro scale,the traditional forming process and theory may fail.Based on the crystal plasticity theory,upsetting tests of micro copper cylinders with different dimensions and grain sizes were simulated,and the decreasing flow stress scale effect was studied and discussed.Results show that with the decrease of billet dimensions,the flow stress is gradually decreased,and the decreasing flow stress scale effect is emerged;with the increase of grain size,the decreasing flow stress scale effect is more remarkable.It can also be seen that the decreasing flow stress scale effect can be well simulated with the crystal plasticity theory,and the necessary relevant information is provided for deeper understanding on this scale effect,as well as the design of processes and die structures in the microforming.
