Non-linear layerwise dynamic response analysis of sandwich plates with soft auxetic cores and embedded SMA wires experiencing cyclic loadings

Non-linear dynamic behavior of sandwich plates with shape memory alloy (SMA) reinforced face sheets and soft auxetic (negative Poisson ratio) cores is investigated in the present article. Plates with stiff or traditional cores may be regarded as special cases. One of superiorities of the present work is considering the localized and instantaneous changes of martensite volume fraction of the individual particles of the SMA wires, through proposing a constitutive law and a cyclic phase-transformation tracing algorithm that are appropriate for pursuing the cyclic loading events and the relevant nested hysteretic pseudoelastic loops due to the plate vibration. Another novelty is incorporation of the core auxeticity and transverse compliance, through an efficient global-local layerwise plate theory. An updating iterative approach is employed to solve the resulting non-linear time-dependent finite element formulation. Results confirm the vibration attenuation due to the loss in the stored energy of the plate that is consumed by the SMA wires during the phase transformation. Moreover, the auxeticity of the core has led to significant stiffening in both the core and plate and consequently, reductions in the lateral deflections of the plate.