On inefficiency of the shape memory alloys in dynamically loaded sandwich plates with structural damping: New 3D zigzag-viscoelasticity theory and asymmetric transformations

The important claim that the presence of the structural damping considerably lessens or even eliminates the effectiveness of the embedded shape memory elements in the dissipation of the vibration/impact energies of the structures, is stated and proven here for the first time. The finite-element-based governing equations of thick composite sandwich plates with homogeneous/FG soft viscoelastic cores and embedded SMA wires are derived based on a new hyperbolic SMA-zigzag sandwich plate theory that considers the transverse flexibility. The tension-compression asymmetry of the SMA behavior and Zener-viscoelasticity-based zigzag nonlinear corrections are implemented to guarantee the transverse stress continuity at the interfaces between layers and updating the relation between the describing parameters of the displacement field, and the stiffness and even mass matrices of the elements within each time step. For the first time, the phase-based rather than the mixture-based stresses are considered in tracing the phase transformations. The resulting time-dependent nonlinear integrodifferential equations are solved by a special algorithm. Results confirm, for the first time, that the stress strain hysteresis loops of the SMAs may shrink or even disappear in presence of the structural damping; so that, the belief that the phase-transformation-based damping and the structural damping directly add to each other, is quite wrong.