Elastoplastic analysis by complete implicit stress-update algorithm based on the extended subloading surface model

Abstract

Elastoplastic analysis of solid structures under cyclic loadings is increasingly required in recent years. To this end, it is necessary to adopt elastoplastic model capable of describing cyclic loading behavior and to employ stress integration algorithm that enables effective and robust calculation. The subloading surface model excluding a purely-elastic domain is capable of describing the cyclic loading behavior in addition to the monotonic loading behavior. The complete implicit stress-update algorithm by return-mapping based on the closest-point projection for the extended subloading surface model is formulated in this article. In addition, the consistent tangent modulus tensor required for the accurate calculation by the return-mapping is formulated in the inverse matrix form. They are implemented into the implicit finite element program through the user-subroutine. We simulate elastoplastic behavior of metals to assess calculation accuracy and efficiency of the proposed algorithm. Numerical experiments for cyclic loading behavior of metals are shown in order to verify the accuracy and the efficiency of the computer program based on the return-mapping and the consistent tangent modulus tensor.

Keywords

• plasticity
• constitutive equation
• finite element method
• return-mapping
• subloading surface model
• consistent tangent modulus tensor
• metals