Dynamics of focused ultrasound actuated shape memory polymers

Abstract

Shape memory polymers (SMPs) are used in a wide range of applications in the fields of medicine, electronics, space technology and textiles among others. Consequently, an emphasis on finding an efficient means of actuating these polymers, especially for sensitive and remote applications becomes important. Focused Ultrasound (FU) induced thermal actuation of SMPs has proven to be a safe, remote and flexible technique of achieving spatially and temporally controllable shape recovery. Increasing research is being done to model the shape memory behavior since it forms the basic necessity for SMP use in any application. However, it has mostly been numerical in nature. In this study, we develop a comprehensive analytical model to understand the dynamics of the FU induced shape recovery of SMPs with a focus on acoustic, medium, material and geometric nonlinearities. We estimate the acoustically induced thermal energy inside the SMP and incorporate that energy in an analytical model to understand the change in temperature dependent mechanical properties of SMP as a result of FU exposure. Using these properties, governing equations of motion for an Euler- Bernoulli SMP cantilever beam are formulated through Generalized Hamilton’s Principle. An analytical solution to trace the recovery of the beam is obtained using method of multiple scales for weak geometric nonlinearities. The model is experimentally validated and is able to successfully give a closed form expression for the amount of shape recovery achieved as a function of acoustic parameters, thus eliminating the need of analyzing any intermediary acoustic, thermal and elastic behavior.