Thermo-mechanical behavior of shape adaptive composite plates with surface-bonded shape memory alloy ribbons

In this paper, thermo-mechanical analysis of rectangular shape adaptive composite plates with surface-bonded shape memory alloy (SMA) ribbons is introduced. A robust phenomenological constitutive model is implemented to predict main features of SMA ribbons under dominant axial and transverse shear stresses during non-proportional thermo-mechanical loadings. The model is capable of realistic simulations of martensite transformation/orientation, reorientation of martensite variants, shape memory effect, pseudo-elasticity and ferro-elasticity effects. A numerical process is addressed to solve the time-discrete counterpart of the model using an elastic-predictor inelastic-corrector return mapping algorithm. Considering small strains and moderately large rotations in the von Kármán sense, governing equations of equilibrium are derived based on the first-order shear deformation theory. A Ritz-based finite element method along with an iterative incremental strategy is developed to solve the governing equations of equilibrium with both material and geometrical non-linearities. The capability of the material and structural model is examined by a comparative study with numerical data available in the open literature for laminated SMA beams. Effects of the pre-strain state, temperature, length and arrangement of the SMA ribbon actuator are investigated, and their implications on the thermo-mechanical behavior of shape adaptive composite plates are put into evidence, and pertinent conclusions are outlined.