Microplane Modeling of Shape Memory Alloys in an Alternative Formulation

In this work, a volumetric-deviatoric split in microplane formulation is considered for modeling of shape memory alloys. In the microplane theory, macroscopic stress tensor is projected into the microplane stresses that are decomposed to either Volumetric-Deviatoric-Tangential (V-D-T) split or Volumetric-Deviatoric (V-D) split. Then 1D constitutive laws are defined between associated microplane stress and microplane strain on any plane. The homogenization process is used according to which macroscopic strain tensor is obtained by integration strains on all orientations at a point. The constitutive formulation based on V-D-T split uses the principle of complementary virtual work (PCVW) to derive macroscopic strain tensor. It is shown that in the microplane models based on V-D-T split — which are derived from the PCVW — the thermodynamic consistency cannot be guaranteed in all loading conditions and the second thermodynamic law might violate. It is shown that a special case of V-D-T split, known as the V-D split, is an effective approach to remedy violation from the second law of thermodynamics. Numerical comparison of the microplane formulation based on V-D-T split and V-D split shows that alternative splits predict the same result in some different loadings. The efficiency of the V-D split is its thermodynamic consistency.