Matrix-presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting

The main purpose of this paper is to develop the matrix presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting to obtain the friction coefficients during the upsetting process. This inverse model assumed the linear material and based on the modified experimental loading increments using the linear modified experimental upsetting loading standard proposed in this paper. Then the friction coefficients of contact boundary between the workpiece and the die at specific finite element analysis stages can be derived. Finally, using the cubic spline fitting, the history of friction coefficient during the upsetting process can be obtained. It is demonstrated that the workpiece profile of upsetting experiment is quite identical to the workpiece profile of simulation using the result obtained in this paper as the history of friction coefficient of contact boundary, and furthermore the distribution of stress and strain of the workpiece during upsetting process can be understood.