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

Abstract

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.

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

“…In thin, displacement-based elements (e.g., when using plate theories), full integration of the stiffness matrices may lead to shear and membrane locking or over-stiff behaviors, especially when highly-constrained boundaries or coarse meshes are used [41][42][43]. These problems are owing to the low number of degrees of the element; so that sides of the element cannot deform in harmony with the resulting deformation field.…”

Localized and overall interaction effects of irregular interfacial bonds and elastic edge restraints for sandwich and functionally graded multilayer circular plates with normal/shear tractions

“…Tornabene et al [13] presented an accurate inter-laminar recovery approach for the refinement of results of the layerwise theories. Recently, Ghaznavi and Shariyat [14] and Shariyat and Ghaznavi [15] presented a dynamic 3D elasticity-based correction for both the stress and displacement components. However, some very limited researchers have used either the 3D elasticity theory or modifications based on this theory, for evaluation of the influence of the interfacial defects in rectangular plates.…”