Date of Award


Publication Type

Doctoral Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering


Engineering, Aerospace.


Green, Daniel (Mechanical, Automotive and Materials Engineering)




This dissertation consists of three major parts. In the first section, the springback simulation of Numisheet&'05 Benchmark#3 was investigated with different material models (Hill's 1948 yield with pure isotropic and mixed isotropic-nonlinear kinematic hardening) using the commercial finite element code ABAQUS. Different theoretical and experimental parameters affecting springback were discussed. In the second section, a new anisotropic material model based on non-associated flow rule (NAFR) and mixed isotropic-nonlinear kinematic hardening was developed and implemented into ABAQUS as a user-defined subroutine. Also, a new direct stress integration formulation applicable to quadratic yield and potential functions (e.g., Hill&'s 1948 anisotropic function) was developed based on the return mapping algorithm. This model is able to consider different aspects of anisotropy and cyclic hardening while maintaining both theoretical and computational simplicity. The model was validated by comparing numerical predictions of material behaviour under different loading conditions (equibiaxial tension, monotonic and cyclic shear) and of mechanical properties (uniaxial yield stresses, r-values) with experimental data. The model was used to simulate cup drawing and plane-strain channel drawing with drawbeads. The results showed that this non-associated, mixed hardening model significantly improves the prediction of earing and springback, even when a rather simple quadratic constitutive model is used. In the third section, two different anisotropic models for sheet materials were compared: (i) the quadratic NAFR model; (ii) a non-quadratic associated model, so-called Yld2000-2d, proposed by Barlat et al. (2003). A new general stress integration scheme applicable to all types of yield and potential functions (quadratic or non-quadratic) and flow rules (associated or non- associated) with mixed hardening, based on the multi-stage backward-Euler return mapping algorithm was developed. Both models were implemented into ABAQUS (for both isotropic and mixed hardening) and used to simulate cup drawing and springback of a plane-strain channel section formed with drawbeads. Cyclic tension-compression tests were performed to determine the mixed hardening parameters. The simulation results predicted with each model were compared and it was shown that both models are able to describe the springback and anisotropic behaviour of sheet materials quite accurately. However, the quadratic NAFR model required significantly less computation time.