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In this work a transformation strain gradient enhancement is introduced into a phenomenological constitutive model for the pseudoelastic behavior of shape memory alloys. The constitutive model is able to capture several unique features of the constitutive response of these materials during the transformation between austenite and martensite during the pseudoelastic response. These features include the asymmetry in the initial transformation stresses in tension versus compression, the asymmetry in the transformation strains in tension and compression, and finally the asymmetry in the hardening behavior in tension and compression. In fact, experiments have shown that untrained NiTi exhibits hardening during its transformation in compression, but softening for tensile loading. It is this softening behavior that motivates the need for the introduction of the transformation strain gradient into the constitutive modeling. Transformation strain gradient effects are introduced via a phase variable that describes the extent of transformation. The free energy of the material then depends on gradients of the phase variable, which introduces a material length scale into the theory. The governing equation for the phase variable is developed from a microforce balance and continuum thermodynamics analysis. The model is implemented in the commercial finite element software Abaqus through user defined subroutines and several numerical simulations are performed to illustrate the model response and lack of numerical mesh-dependency of the results. 

A novel experimental setup is presented that allows for precise control of thermal and mechanical loads, and simultaneous monitoring of the temperature and the full-field deformation of small SMA structures that undergo phase transformations. The facility is used to conduct two experi- ments in which NiTi tubes are taken through a temperature cycle under constant load that leads to phase transformations in the form of helical localization bands that propagate along the specimen. The latent heat of transformation causes a complex interaction with the prescribed load and thermal environment. By changing the rate of the airflow through the environmental chamber it is revealed that the velocities of the transformation fronts depend on the rate at which heat is removed/added by the controlled environment. The experiments are simulated using a new fully coupled thermomechanical extension of the constitutive framework developed by this research group. Key features of the framework include the modeling of the reversible A⇄M transformation through a single surface in the deviatoric stress-temperature space that obeys kinematic hardening; with the transformation strain and entropy as the internal variables gov- erned by an associative flow rule; and the inhomogeneous deformation exhibited in tension being modeled as softening. The tube is analyzed in a finite element coupled static displacement transient temperature analysis, and taken through the cool/heat cycle of the experiment. The temperature-strain response is accurately reproduced with the two transformations initiating at essentially the same temperatures as in the experiment and propagating in similar localized banded manners at similar speeds. Reproduction of the complex behavior observed in the ex- periments requires the calibration of the constitutive model, its discretization, and the modeling of the structure and its boundary conditions to work together to near perfection. The simulation also demonstrated that the heat exchange between the structure and the environment, in the present analysis governed by only by convection, requires further enhancement.