Simulation of strain localization in metal forming processes using bilinear mixed u/p elements

In this study, a large deformation finite element approach for numerical analysis of the strain localization is developed based on the concept of mixed interpolation of displacement/pressure. This finite element approach is suitable for the material constitutive relation in rate form. In order to avoid oscillatory behavior and path dependence observed in some traditional stress rates, the Truesdell stress rate is employed in the integration of the constitutive equation. The corresponding consistent tangent stiffness is derived to maintain the asymptotically quadratic convergence of the Newton-Raphson iterative scheme used in the solution of the implicit equilibrium equations. To illustrate the performance of the proposed element, the numerical simulation of three example cases has been carried out and the result shows that the element is of good capability to capture strain localization especial when remeshing operation is required.