Original Article

A modified constitutive model based on Hill48 function for the forming analysis of orthotropic sheet metal

¹ School of Mechanical Engineering, Yancheng Institute of Technology, Yancheng, PR China
² Jiangsu Dayang Precision Forging CO., Ltd

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 13 November 2025
Accepted: 25 November 2025

Abstract

Sheet metal forming prediction is a research frontier in the field of high-end equipment such as automobile and aerospace, especially the anisotropy of sheet metal caused by rolling process. How to balance the prediction accuracy and application convenience of anisotropic constitutive model has not been effectively solved. In this study, by introducing the azimuth of the stress principal axis, the anisotropic parameters determination method for coupling multi-dimensional stress and r-value experimental data was given, and the Hill48 modified model with the prediction accuracy of the high-order yield equation which can be applied to the associated flow criterion was established. The modified model improved the ability to characterize different stress states according to the characteristics of sheet metal forming, and the asymmetric stress state between uniaxial and symmetric biaxial stress states was described by interpolation functions. Hill48 modified model was developed to ABAQUS/VUMAT finite element code to simulate the deep drawing process of cylindrical cup and square box. The results show that the developed model can clearly reveal the influence of different stress states on the forming parts, and significantly improve the forming prediction accuracy. This study provides an idea for overcoming the problem of anisotropic yield model considering both application convenience and prediction accuracy, and has important theoretical significance and application value for the development of forming technology of complex components.