Modeling of simultaneous shape memory and pseudoelastic effects of shape memory alloys on nonlinear dynamic response of multilayer composite plate embedded with pre-strained SMA wires under thermal condition

Shape memory alloys as a kind of smart materials, have two unique characteristics entitled shape memory and pseudoelastic effects. In this paper, a nonlinear dynamic analysis of multilayered composite plate embedded with pre-strained SMA wires under thermal condition is implemented considering both effects of SMAs simultaneously, for the first time. The constitutive equation proposed by Brinson is used for modelling the behaviors of SMA wires. In this work, equations of motion are derived in the framework of Carrera's Unified Formulation, for robust analysis of the problem. In this regard, the nonlinear strains are employed for modelling the thermal effects and also the effect of recovery stresses in the SMA wires. In this study not only the material properties are instantaneous variable with respect to the time and location, but they are also unknown, which make the problem more complicated. For this aim, a transient nonlinear finite element in conjunction with incremental iterative algorithm proposed by the author is employed, in order to solve the equations. Results show that upon the thermal condition, the recovery stress is generated in the SMA wires and therefore reduce the amplitude of a damped response of the plate. One conclusion from this study is that, in contrast with many studies reported before, it cannot be always say that the stress recovery in SMA wires is increased with increasing the pre-strain of SMA wires. In other words, for a specified increasing in temperature, only a limit amount of pre-strain comes back to its original shape and not more. Also, several numerical examples upon effect of different thermal condition, different volume fraction of SMA wires and different boundary conditions have been analyzed.