Modeling and analysis of reversible shape memory adaptive panels

The aim of this article is to model and analyze reversible shape adaptive panels integrated with one-way shape memory alloy actuators and to examine the effects of martensite variants reorientation. A robust three-dimensional macroscopic model is implemented to simulate shape memory effect, pseudo-elasticity, and ferro-elasticity features of shape memory alloys. The shape memory alloy constitutive model provides analytical closed-form solutions for self-accommodation and martensite reorientation mechanisms while proposing an iterative solution scheme for martensite transformation or orientation assuming an exponential form for transformation kinetics. The finite element formulations are derived based on the first-order shear deformation theory considering the modified Sanders shell assumptions and including geometrical nonlinearity in the von Kármán sense. An iterative incremental procedure on the basis of the elastic-predictor inelastic-corrector return mapping algorithm is introduced to solve the coupled governing equations of equilibrium with both material and geometrical nonlinearities. The numerical illustrations emphasize the feasibility of reversible shape adaptive panels integrated with thermally activated pre-strained one-way shape memory alloy ribbons or layers. Effects of martensite reorientation, pre-strain, temperature, arrangement, and dimension of shape memory alloys as well as of thermal cycles are investigated, and their implications on the performances of reversible shape adaptive spherical panels are highlighted, and pertinent conclusions are outlined.