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This work presents a three-dimensional constitutive model for the martensitictransformation in polycrystalline Shape Memory Alloys (SMAs) under largedeformation. By utilizing the logarithmic strain and rate, the model is able toaccount for large strains and rotations that SMA-based components mayundertake, but also resolves the artificial stress errors caused by thenon-integrable objective rates that are widely used in current commercialfinite element software. The model is developed through classical thermodynamiclaws combined with the standard Coleman-Noll procedure. The scalar martensiticvolume fraction and the second-order transformation strain tensor are chosen asthe internal state variables to capture the material response exhibited bypolycrystalline SMAs. A detailed implementation procedure of the proposed modelis described through a user-defined material subroutine. Numerical experimentsconsidering SMA components including a bar, a beam, a torque tube and a solidflexible structure under stress/thermally-induced phase transformations areinvestigated via the proposed model, and the results under cyclic loading arecompared against the predictions provided by the Abaqus nonlinear solver. Thedevelopment framework of the proposed model and its implementation procedurecan be extended to incorporate other nonlinear phenomena exhibited by SMAs,such as transformation-induced plasticity, viscoplasticity, and damage underlarge deformation.

A three-dimensional constitutive model for the martensitic transformation in polycrystalline shape memory alloys under large deformation