A new nonlinear finite element model for transient dynamic response of a micro composite plate embedded with micro SMA wires considering the size effects

Abstract

In this research, a nonlinear dynamic analysis of micro plate containing micro shape memory alloy (SMA) wires, taking into account the material and geometric nonlinear effects and also considering the instantaneous changes of martensitic volume fraction (MVF) in different points of the micro plate, has been investigated. In this study, using the first-order shear deformation theory (FSDT) and applying Hamilton's principle, the governing equations of micro plate are extracted such the kinematic equations of micro SMA wires are coupled with governing equations. In this regard, von Karman nonlinear strain-displacement relation is used to consider large displacements and the model proposed by Hernandez and Lagoudas is employed to model the pseudoelastic behavior and also to capture the size effect of the SMA wires at micro scale. The modified couple stress theory is also employed to consider the size effect on the matrix material of micro plate. In addition, it is assumed that the micro wires are arranged in FG forms in the direction of the thickness of the micro plate. Using the return mapping algorithm and nonlinear finite element method, the governing equations of motion, are solved. In the results section, the study of parameters such as size effects, different boundary conditions, taking into account nonlinear strain field, diameter change and type of arrangement of micro SMA wires, length scale factor and thickness of micro plate, have been implemented. To evaluate the validity of the present work, some of the results are compared with the articles available in the literature. New results show that the bigger diameter of the micro SMA wires (considering the total volume fraction constant) and the smaller length scale factor, the higher damping ratio of the micro plate is obtained. Also, the vibration damping ratio increases when more micro SMA wires are arranged in $FG\mathrm{}–\mathrm{}X$ form.

Keywords:

• Micro shape memory alloy wire
• Hernandez and Lagoudas model
• modified couple stress theory
• nonlinear finite element model
• size effects