## 4 Conclusions  
A novel analytic elastic-plastic method based on the Cazacu-Barlat 2004 yield function and isotropic hardening was developed to investigate the bending and springback behaviour of asymmetric materials. Compared to existing methods, the proposed analytical method can be an effective tool to simplify springback prediction of asymmetric sheet metals. 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. As a case study, pure bending of stainless steel 304 and DP980 was investigated analytically and numerically. In addition, the V-bending of the stainless steel 304 plates was studied numerically, and the analytical method was modified. The following conclusions can be drawn based on the comparison of the analytical and numerical outputs of the experimental results:  
1. The comparison of the analytical and experimental results shows that for pure bending, the new method can successfully capture TCA of the materials with less material parameters;  
2. The linear and nonlinear springback of SUS304, determined based on the analytical method, showed great agreement with the experimental results;  
3. Implementing the analytical method into the UMAT subroutine, the springback results from the V-bending simulation of SUS304 were a great match with the experimental results. By applying TCA effects in calculations, the relative error was reduced from \(-7.86\) to \(-2.11\%\) and \(23.01\) to \(4.32\%\) for TD and RD bending, respectively.  
4. From simulations, it was observed that, in V-bending of SUS304, the springback increased by increasing the friction coefficient, depending on the bending radius and the material properties. In addition, it was observed that the numerical and analytical springback values were almost the same at higher friction coefficients, and the analytical method can be modified for lower friction coefficients.  
5. The modified analytical method can successfully predict the springback behaviours of 16 types of SUS304 in the V-bending process, and the results were consistent the with experimental results.  
Conceptualisation, H.M. and R.Y.; methodology, H.M. and R.Y.; software, H.M.; validation, H.M. and R.Y.; formal analysis, H.M.; investigation, H.M. and R.Y.; resources, R.Y. and B.W.; data curation, H.M. and R.Y.; writing--original draft preparation, H.M.; writing--review and editing, R.Y. and B.W.; visualization, H.M.; supervision, R.Y. and B.W.; project administration, R.Y. and B.W.; funding acquisition, R.Y. and B.W. All authors have read and agreed to the published version of the manuscript.  
The first author was supported by the Postgraduate Scholarship Awards provided by the Western Sydney University, Australia. This research received no external funding.  
Figure 16: Comparisons of experimental and analytical springback in V-bending for SUS304 with different material strengths.  
**Acknowledgments:** All the co-authors, H.M., R.Y. and B.W., would like to show their gratitude to the School of Engineering, Western Sydney University for the support and assistance with their research activities.  
**Conflicts of Interest:** The authors declare no conflict of interest.