A novel theoretical model for a laminate cantilever beam consisting of numerous superelastic shape memory alloy (SMA) layers, based on the ZM model and Timoshenko theory is introduced. The mathematical equations are first developed to predict and describe the internal material structure of laminated beam, according to the solid phase transformation in SMA layers. Then, the theoretical expression of the moment and shear force for a superelastic SMA composite cantilever beam is derived. The proposed model is validated against a 3D finite element analysis model (FEA), giving very good agreement in each case. The moment-curvature response, and distribution of martensite volume fraction and axial stress along the beam length are investigated.
KEYWORDS: Shape memory alloys, Composites, Electroluminescence, Finite element methods, 3D modeling, Testing and analysis, Energy harvesting, Beam shaping, Chemical elements, Analytical research
We propose an analytical model for a laminated beam consisting of a superelastic shape memory alloy (SMA) core layer bonded to two piezoelectric layers on its top and bottom surfaces. The model accounts for forward and reverse phase transformation between austenite and martensite during a full isothermal loading-unloading cycle starting a full austenite in the SMA layer. In particular, the laminated composite beam has a rectangular cross section and is fixed at one end while the other end is subjected to a concentrated transverse force acting at the tip. The moment-curvature relation is analytically derived. The generated electric displacement output from the piezoelectric layers is then determined using the linear piezoelectric theory. The results are compared to 3D simulations using finite element analysis (FEA). The comparison shows good agreement in terms of electric displacement, in general, throughout the loading cycle.
KEYWORDS: Shape memory alloys, Composites, Finite element methods, Electroluminescence, 3D modeling, Numerical analysis, Beam shaping, Epoxies, Chemical elements, Sun
We present a numerical solution for a smart composite beam consisting of an epoxy matrix reinforced with unidirectional superelastic shape memory alloy (SMA) fibers with uniform circular cross section. The beam is loaded by a tip load, which is then removed resulting in shape recovery due to superelasticity of the SMA wires. The analysis is carried out considering a representative volume element (RVE) of the beam consisting of one SMA wire embedded in epoxy. The analytical model is developed for a superelastic SMA/epoxy composite beam subjected to a complete loading cycle in bending. Using the proposed model, the moment-curvature profile, martensite volume fraction variation, and axial stress are determined. The results are validated against three-dimensional finite element analysis (3D FEA) for the same conditions. The proposed work is a contribution toward better understanding of the bending behavior of superelastic SMA-reinforced composites.
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