RIGID‐PLASTIC IMPLICIT SCHEME FOR NON‐ AND THREE‐DIMENSIONAL ANALYSIS OF METAL FORMING BY FINITE ELEMENT METHOD

This paper is devoted to the analysis of metal forming with assumption of rigid‐plastic behaviour with strain hardening. As opposed to the classical rate problem formulation based on Markov's principle and the explicit scheme, a more satisfactory incremental approach is deduced from Moreau's catching up algorithm. This implicit scheme, although more complicated, gives better results concerning convergence and numerical stability. Using an internal variable representing the strain hardening, an incremental strain energy density is defined which leads to a principle of minimum of the total incremental strain energy. In the numerical approximation using finite elements, the non‐linear equilibrium equations are solved by classical Newton's method. An approximation of Coulomb's criterion is used in order to represent friction with a rigid foundation. The simple compression test is simulated and shows that the implicit scheme is faster than the explicit one.