## 1 Introduction  
Over the last decade, due to the development of advanced materials and manufacturing technologies, sheet metal forming has become more challenging for industry sectors and researchers. This manufacturing process has a wide range of applications in automobile parts, electronic parts, food and drink cans, etc. Bending is a widely used forming process in sheet metal forming which is usually accompanied with an unwanted springback phenomenon. Springback is one of the most challenging issues in sheet metal forming. Accurate prediction of springback helps manufacturing industries to design appropriate tools to compensate for this effect and enhance the dimensional accuracy of the finished parts [1]. Anisotropy in plastic behaviour is a common phenomenon in metal forming. An initial anisotropy in yield points and the subsequent hardening behaviour can be caused by tension-compression asymmetry (TCA) [2, 3]. Several metals have been reported to have asymmetrical yield surface due to the fact of their eccentricity in yielding or in their subsequent hardening. Hexagonal closed pack (HCP) metals, such as magnesium alloys, have strong asymmetry due to the fact of their limited slip systems and the strong basal texture [4]. Cubic materials, such as body-centred cubic (BCC) and face-centred cubic (FCC) metals, are usually considered as symmetrical materials. However, some cubic metals are reported to exhibit TCA too. [PERSON] et al. [5] designed a special testing apparatus and performedin-plane tension and compression experiment tests on a copper alloy sheet. They showed that copper alloy exhibits TCA. [PERSON] et al. [6] performed in-plane tension and compression experiments on SUS304 sheets in the rolling direction (RD) and transverse direction (TD). In addition, they performed pure bending and V-bending experiments on the sheets to understand the effects of TCA on bending and springback behaviours. They showed that the TCA of the material has considerable effects on the bending and springback behaviours of the material. Recently, [PERSON] et al. [7] reported the strength differential effect (SDE) for DP980 steel sheet by performing in-plane tension and compression and pure bending experiments. In order to consider the abovementioned asymmetry in constitutive equations, two different methods were proposed by researchers. The first method is to suppose an initial translation of yield surface by adopting non-zero back stress in the combined isotropic-kinematic hardening model [4; 8; 9; 10]. For example, [PERSON] et al. [4] used the two-surface model for magnesium alloy sheets. [PERSON] et al. [9] proposed a model based on a distortional hardening approach which can extend the initial yield function and hardening asymmetry under different loading condition. More recently, [PERSON] et al. [11] proposed a criterion for anisotropic hardening considering the strength differential effect based on non-associated flow rule. The other method is to introduce an asymmetric yield function, which is stress or invariant of stress dependence. For example, [PERSON] [12] added linear stress terms into [PERSON]'s 48 yield surface. [PERSON] and [PERSON] [13] modified the isotropic Drucker yield criterion [14] by applying the second and third invariants of stress to describe the initial tension-compression yield asymmetry. [PERSON] et al. [15] proposed a general asymmetric yield function with a dependence on the first stress invariant for pressure-sensitive metals. Few analytical studies are available regarding the bending and springback of metals with TCA. [PERSON] et al. [16] studied pure bending and bending under tension of AZ31B magnesium alloy sheet analytically by approximating the stress-strain curve of the magnesium alloy sheets. They applied discrete linear hardening rules in each deformation region to determine the moment-curvature and the springback of the material. [PERSON] et al. [17] studied the sidewall curve of magnesium alloy AZ31B under bending/unbending.