Elastoplastic analysis by return-mapping method with rigorous loading criterion for extended subloading surface model

Abstract

The extended subloading surface model is capable of describing cyclic loading behavior accurately. The elastoplastic deformation analysis by the finite element analysis can be executed efficiently by the complete implicit stress integration method with the return-mapping and the consistent tangent modulus tensor. The subloading surface model has been applied to the FEM analysis with the return-mapping method. However, the implicit stress integration procedure with the loading criterion used in the past works is applicable only to the description of monotonic loading process so that it causes the erroneous calculated result in the cyclic loading process. The rigorous loading criterion is adopted in this article. The validity of the implicit stress integration procedure adopting the loading criterion will be verified in forward and inverse loading processes for strain increments to various directions. The implicit calculations by the return-mapping method are performed adopting the past and the rigorous loading criterions in the monotonic and the reverse loadings under the bi-axial loading state in this article. Eventually, it may be stated that the accurate numerical solution can be attained by adopting the rigorous loading criterion for the general loading process in the multi-axial stress and/or strain state.

Keywords

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