## 1 Introduction
They introduced a semi-analytical bending/unbending method to determine the bending moment-curvature diagrams for different values of tensile back forces. [PERSON] et al. [5], [PERSON] et al. [6] and [PERSON] et al. [7] calculated the bending moment-curvature diagrams for pure bending tests based on stress-strain (SS) curves obtained from in-plane tension-compression tests. They divided the sheet thickness of the specimen into 100 thin layers and found the stress of each layer from the SS curves in tension and compression under a uniaxial condition. All the analytical studies mentioned above are semi-analytical methods which are based on piecewise fitting of the SS curves of materials without using key factors of continuum plasticity such as yield surface or flow rule. Therefore, their methods have too many parameters related to the SS curves in tension and compression, and also intensive calculations are needed. [PERSON] and [PERSON] [18] presented a simple analytical solution for pure bending of hexagonal closed-packed metals without considering the effects of neutral surface shift. In this study, a novel analytical method is proposed for steels, which is based on uniaxial, elastic-plastic bending by applying the Cazacu-Barlat 2004 asymmetric yield function and considering the neutral surface shift. This method uses only the material parameters in tension, along with an asymmetry coefficient related to the yield function. Hence, it can greatly simplify the analytic and numerical studies of metal sheet forming. The proposed analytical method can significantly simplify the springback prediction of asymmetric sheet metals, compared to those existing methods. This method can be an effective tool for manufacturing industries dealing with springback during sheet metal forming processes such as bending, deep drawing, roll forming, etc. This new method can be used for analytic study and numerical analysis by implementing it into the commonly used commercial finite element analysis package--Abaqus/Standard via user-subroutine UMAT. In order to show the versatility of the new method, pure bending and V-bending of steels were investigated as two case studies. In the pure bending, moment-curvature diagrams of SUS304 and DP980 were analytically calculated. Furthermore, linear and nonlinear springback values of SUS304 were also analytically determined and compared with experimental results available in the literature [6]which show great agreement. By using the UMAT, the finite element model of the pure bending was devised, and the obtained numerical results were in good agreement with the analytical and experimental results. In the second case, V-bending, the effects of TCA on the springback behaviour of SUS304 plates were investigated numerically. The springback results from the simulations with and without TCA effects were compared with those experimental results from the literature. The results show that springback prediction improved significantly by considering the TCA of the material. Finally, the analytical method was modified for prediction of springback in V-bending. Based on this method, the springback values of 16 types of SUS304 with different strengths were calculated and compared with those from the experiments. The predicted springback behaviours were consistent with the experimental results. This paper is outlined in the following sections. Section 2 provides a detailed development of the proposed analytical method. Section 3 explains the numerical method and discusses the analytical and numerical results in detail, and, finally, Section 4 gives comprehensive conclusions based on the research findings obtained.