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

This work presents a three-dimensional constitutive model for the martensitic\ntransformation in polycrystalline Shape Memory Alloys (SMAs) under large\ndeformation. By utilizing the logarithmic strain and rate, the model is able to\naccount for large strains and rotations that SMA-based components may\nundertake, but also resolves the artificial stress errors caused by the\nnon-integrable objective rates that are widely used in current commercial\nfinite element software. The model is developed through classical thermodynamic\nlaws combined with the standard Coleman-Noll procedure. The scalar martensitic\nvolume fraction and the second-order transformation strain tensor are chosen as\nthe internal state variables to capture the material response exhibited by\npolycrystalline SMAs. A detailed implementation procedure of the proposed model\nis described through a user-defined material subroutine. Numerical experiments\nconsidering SMA components including a bar, a beam, a torque tube and a solid\nflexible structure under stress/thermally-induced phase transformations are\ninvestigated via the proposed model, and the results under cyclic loading are\ncompared against the predictions provided by the Abaqus nonlinear solver. The\ndevelopment framework of the proposed model and its implementation procedure\ncan be extended to incorporate other nonlinear phenomena exhibited by SMAs,\nsuch as transformation-induced plasticity, viscoplasticity, and damage under\nlarge deformation.\n