Fast Plastic Integration Algorithms for Forming Process Simulations

Abstract

This paper presents a fast plastic integration algorithm and compares it with other algorithms for forming process simulations. The iterative Return Mapping Algorithm (RMA) is widely used owing to its accuracy and efficiency, but it is still time consuming and may cause divergence problems. Another algorithm based on the Incremental Deformation Theory (IDT) was proposed, using the deformation theory of plasticity by piecewise; it is very fast but could not well consider the loading history, leading to notable errors. The new Direct Scalar Algorithm (DSA) based on the flow theory of plasticity is proposed in this paper. The basic idea is to transform the constitutive equations in terms of the unknown stress vectors into a scalar equation in terms of the equivalent stresses which can be determined by using the experimental tensile curve; thus, the plastic multiplier λ can be directly calculated without iterative solution. The DSA is a fast and robust plastic integration algorithm. The comparison of the results obtained by using the three algorithms shows the accuracy and efficiency of the DSA.