Nonlinear Quasi-static Investigation of Microbeam Embedded with Micro SMA Wires Considering Size Effects and Phase Transformation

Introduction: The size effect on the quasi-static analysis of microbeams embedded with micro shape memory alloys (SMAs) has not been studied as per today. Therefore, in the present research, the nonlinear bending performance of the microbeam comprising SMA micro SMA wires is implemented considering the size effects regarding the coupled geometric and material nonlinearities for the first time. The SMA has different properties depending on the amount of strain at each point of the microbeam. Moreover, the amount of strain depends on the SMA properties. This mutual dependence between SMA properties and strain leads to increased complexity in the analysis. Methods: In this research, the formulation presented by Lagoudas and Hernandez is used for modeling the phase transformation and capturing the size effects for the SMA microwires. Via the modified couple stress theory, the size effect of the matrix material is captured. Result: The nonlinear equations of motions are obtained by the principle of virtual work, using the von Karman strains and, Timoshenko beam theory for different boundary conditions. Then the return mapping scheme and also iterative nonlinear finite element methods were used for solving the governing equations. The results are presented according to the distribution of martensitic volume fraction (MVF), transverse deflection, distribution of strain, stress-strain graph, and variations of the elasticity modulus of the embedded micro SMA wires. A comparison of some obtained results with available references indicates the present work’s validity. Conclusion: One of the most important findings of this work is that increasing the value of the length-scale factor as well as increasing the diameter of the micro SMA wires will reduce the maximum transverse deflection of the microbeam.