This thesis is a summary of my research works at the MSM department of the University of Liège since 1989. These research works are devoted to the numerical simulation of the three-dimensional sheet metal forming processes by the finite element method. Several research areas, including the finite element modelling, the time-integration technique of material constitutive laws and the 3D contact treatments are covered. The theoretical methodologies, the numerical implementation and industrial applications will be presented.
The thesis begins with a brief overview made in chapter 1.
In chapter 2, a 8-node mixed brick element based on the HU-WASHIZU variational principle is developed (JET3D element). Special attention is paid to avoid hourglass modes as well as locking phenomena, including "shear locking" and "volumetric locking" in nonlinear analysis. Numerical examples are used at the end of this chapter to assess the performance and applicability of this element.
In chapter 3, a 3D four-node shallow element, which was originally developed by Ph. JETTEUR and then has been improved by him and his co-workers, is recalled (COQJ4 element). Special care is taken to the finite rotation problems and a new formulation for the finite rotation is developed. An example is used at the end of the chapter to show the performance of the proposed formulation for the finite rotation problems.
A special contact element is developed for the shell element in chapter 4. In this chapter, some basics aspects of numerical tretments of contact problem are discussed and some attentions are paid to the contact searching algorithms, which has proved to be very important in 3D cases.
In chapter 5, the appropriate constitutive equations are examined together with the techniques of time-integration and the evaluation of the tangent stiffness matrix. Much attention is paid to the implicit integration methods, which have proved to be very efficient for large increments of deformation.
Finally, in chapter 6, two benchmark tests are used as validation of the code. Special attention is paid to the possibility of using dynamic explicit procedure in the numerical simulation of sheet metal forming, although it is often characterised as a quasi-static process.
All the developments made in the thesis have been implemented into the finite element code LAGAMINE developed since 1982 at the MSM department of the University of Liège.