A NUMERICAL-METHOD FOR INTRODUCING AN ARBITRARY YIELD FUNCTION INTO RIGID-VISCOPLASTIC FEM PROGRAMS

Many standard yield functions (Hill, von Mises, etc, ...) allow the de rivation of simple equations relating the effective strain rate to pri ncipal strain rates explicitly. Such yield functions are easily implem ented in rigid-viscoplastic finite element method programs. Other yiel d functions (hosford, e.g.) do not allow for this simple approach. A n umerical method was proposed in this paper to solve this problem which meets the requirement of rigid-viscoplastic finite elements and can g enerate the material stiffness terms (first and second derivatives of the effective strain rate with respect to principal strain rates) at a ny strain state. The numerical method was found to be numerically effi cient, accurate and robust. As an examole of the procedure, Hosford's yield function was introduced in a rigid-viscoplastic finite element p rogram and results for the punch stretching simulation were compared w ith Hill-type materials. The numerical efficiency of the method was al so compared. Simulation of full dome formability test, plane strain an d square punch stretching was performed by this numerical method with Hosford's yield function.