A robust algorithm for behavior and effectiveness investigations of super-elastic SMA wires embedded in composite plates under impulse loading

The spatial and time variations of the martensite volume fraction due to the localized and time variations of the stress distribution along shape memory alloy wires embedded in composite plates have not been considered in the majority of the available researches. In the present research, an accurate algorithm is proposed to determine the localized time variations of the martensite volume fraction and carefully assess the sudden changes in the magnitudes of the induced stresses and strains, and consequently, the effectiveness of the SMA wires, under the impulse loadings. The governing finite element equations of motion of the hybrid composite plate are derived based on Hamilton's principle. The resulting non-linear and piecewise-defined time-dependent finite element formulation is solved through a FORTRAN code, employing Newmark's numerical procedure to evaluate the dynamic responses of the plate. Results reveal that unlike almost all of the available reports, the shape memory alloy wires embedded in the composite host plate cannot always strengthen the plates. Indeed, the behavior of the SMA wires is governed by two opposite phenomena: the significant degradation in the elastic modulus due to the austenite to martensite phase-transformation and the hysteretic behavior due to super-elasticity that consumes the strain energy in the phase-transformation process and leads to smaller stresses and lateral deflections. Therefore, when elasticity modulus of the host plate is higher than that of the SMA, the super-elasticity advantage cannot compensate the disadvantage of the degradation in the elastic modulus and leads to a plate with inferior performances.