Abstract
AbstractMany standard yield functions (Hill, von Mises, etc,…) allow the derivation of simple equations relating the effective strain rate to principal strain rates explicitly. Such yield functions are easily implemented in rigid–viscoplastic finite element method programs. Other yield functions (Hosford, e.g.) do not allow for this simple approach. A numerical method was proposed in this paper to solve this problem which meets the requirement of rigid–viscoplastic finite elements and can generate the material stiffness terms (first and second derivatives of the effective strain rate with respect to principal strain rates) at any strain state. The numerical method was found to be numerically efficient, accurate and robust. As an example of the procedure, Hosford's yield function was introduced in a rigid–viscoplastic finite element program and results for the punch stretching simulation were compared with Hill‐type materials. The numerical efficiency of the method was also compared. Simulation of full dome formability test, plane strain and square punch stretching was performed by this numerical method with Hosford's yield function.
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