Shape-memory alloys: Stress-induced phase transformation, constitutive model, and nonlinear finite-element formulation

Growing applications of shape-memory alloys (SMAs), which possess the capability to remember their original shape after large deformations without undergoing permanent plastic deformation, demand computationally efficient constitutive models and the three-dimensional finite-element formulation to design SMA-based devices in the mechanics community.; In this thesis, the finite-element formulation is based on the mixed three-field Fraeijs de Veubeke-Hu-Washisu (FHW) variational principle to treat several element-locking problems such as shear locking in bending of thin structures; and volumetric locking during inelastic flow in plastic or shape-memory materials. Because of the volume-conserving effects of shape-memory alloys under transformation flow and the shear locking effects in thin structures, the appropriate finite-element formulation is needed. We used the solid-shell finite element formulation incorporating the enhanced assumed strain (EAS) based on three-dimensional three-field mixed formulation to take account of the incompressibility and shear locking problems in the element with appropriate EAS parameters. The element formulation has only a displacement degree of freedom.; The constitutive model developed is thermodynamically admissible, i.e., the model does satisfy Clausius-Duhem inequality. Based on the thermodynamic description, a macroscopic constitutive relation of shape-memory alloys is given by its Helmholtz free energy which is decomposed into elastic and inelastic parts, in analogy to the conventional plasticity. Transformation function is also determined from the internal entropy production rate and transformation flow is associated with transformation function in stress-temperature space. The direction of transformation flow rule is normal to the transformation surface in stress-space so that the transformation surface is expanding isotropically in stress deviator during the martensite transformation deformation, and is similar to the case of the J2 flow plasticity of isotropic hardening law. In the discretized constitutive model, we also present a return-mapping algorithm as a special case of the closest-point projection schemes to be implemented into finite-element formulation.; Numerical results for the given specimen subject to the tensile are also provided to show qualitatively the ability of the present model and to compare quantitatively with other models in uniaxial testing. In order to show the computational efficiency of solid-shell element, we test our constitutive model in simply-supported bending problems and in thin shell structure too. In all the tested cases, the results from the solid-shell element are compared with the results from the pure displacement-based twenty-node element. For the given tests, the proposed model shows an improvement of Newton-Raphson iteration schemes to solve the system of equations and results in numerical efficiency in computational procedures.