A fast method called the “inverse approach” for sheet forming modeling is based on the assumptions of the proportional loading and simplified tool actions. To improve the stress estimation, the pseudo-inverse approach was recently developed: some realistic intermediate configurations are geometrically determined to consider the deformation paths; two new efficient algorithms of plastic integration are proposed to consider the loading history. In the direct scalar algorithm (DSA), an elastic unloading-reloading factor γ is introduced to deal with the bending-unbending effects; the equation in unknown stress vectors is transformed into a scalar equation using the notion of the equivalent stress, thus the plastic multiplier Δλ can be directly obtained without iterative resolution scheme. In the γ-return mapping algorithm, the equivalent plastic strain increment estimated by DSA is taken as the initial solution in Simo’s return mapping algorithm, leading to a stable, efficient, and accurate plastic integration scheme. The numerical experience has shown that these two algorithms give a considerable reduction of CPU time in the plastic integration.
Articles you may be interested inForging tool shape optimization using pseudo inverse approach and adaptive incremental approach AIP Conf. Proc. 1532, 95 (2013); 10.1063/1.4806812Numerical modeling of axi-symmetrical cold forging process by "Pseudo Inverse Approach" AIP Conf.Abstract. This paper presents a simplified numerical method called "Pseudo Inverse Approach" (PIA) for damage prediction in metal forging process modeling and optimization. The approach is based on the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths. Based on the equivalent stress notion and tensile curve, a robust direct algorithm of plasticity is formulated and implemented. The plasticity is coupled with the ductile damage by using a strain based ductile damage model. The forging results obtained by the PIA are compared to those obtained by an incremental approach to show the efficiency and accuracy of the PIA, as well as the abilities to make the damage prediction.
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