Influence analysis of phase transformation anisotropy of shape memory alloy wires embedded in sandwich plates with flexible cores by a third-order zigzag theory with dynamic three-dimensional elasticity corrections

This paper is devoted to the investigation of the effects of the realistic tension–compression asymmetry and anisotropy of phase transformations of shape memory alloy wires embedded in composite sandwich plates with auxetic cores on the resulting nonlinear vibrations. A third-order zigzag description of the displacement field that takes into account the thickness variations of the flexible core and a novel three-dimensional dynamic elasticity stress and displacement correction is proposed and employed. The governing equations are extracted based on Hamilton’s principle and solved using an iterative finite element procedure. A comprehensive phase transformation algorithm and a constitutive model that are capable of accurately tracking the nested hysteresis loops and sub-loops and reverse loading of the shape memory alloy are proposed, considering the tension–compression anisotropy. Interactions of the core compliance, auxeticity, and especially, the transformations anisotropy on the dynamic responses are studied numerically and three-dimensional plots are presented for distributions of the martensite volume fraction. Results show that the realistic tension–compression anisotropy of the shape memory alloy material leads to results that are quite different from those based on the assumption of the symmetry of the material properties and significantly increases the differences between the damping roles of the shape memory alloy wires of the upper and lower layers of the sandwich plate.