The Simulation of Robot Based Incremental Sheet Metal Forming by Means of a New Solid-Shell Finite Element Technology and a Finite Elastoplastic Model with Combined Hardening

The principle of robot based incremental sheet metal forming is based on flexible shaping by means of a freely programmable path-synchronous movement of two tools, which are operated by two industrial robots. The final shape is produced by the incremental infeed of the forming tool in depth direction and its movement along the geometry’s contour in lateral direction. The main problem during the forming process is the influence on the dimensional accuracy resulting from the compliance of the involved machine structures and the springback effects of the workpiece. The project aims to predict these deviations caused by resiliences and to carry out a compensative path planning based on this prediction. Therefore a planning tool is implemented which compensates the robot’s compliance and the springback effects of the sheet metal. Finite element analysis using a material model developed at the Institute of Applied Mechanics (IFAM) [1] has been used for the simulation of the forming process. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamical setting. It is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening which is widely adopted as capable of representing the above metal hardening effects. The major problem of low-order finite elements used to simulate thin sheet structures, such as used for the experiments, is locking, a non-physical stiffening effect. Recent research focuses on the large deformation version of a new eight-node solid-shell finite element based on reduced integration with hourglass stabilization. In the solid-shell formulation developed at IFAM ([2], [3]) the enhanced assumed strain (EAS) concept as well as the assumed natural strain (ANS) concept are implemented to circumvent locking. These tools are very important to obtain a good correlation between experiment and simulation.