A three-dimensional shape memory alloy/elastomer actuator

This paper presents a mathematical model for analysis of a thermally-driven shape memory alloy (SMA)/elastomer actuator under arbitrary loading and boundary conditions. The actuator is a three-dimensional laminated composite box beam that consists of SMA and elastomer layers with a uniform rectangular cross section. The thermomechanical behavior of SMA layers is modeled utilizing Tanaka and Nagaki's constitutive equation and linear phase transformation kinetics. The behavior of the elastomer layers is assumed to be thermoelastic, in which the elastic modulus is considered to be temperature dependent. The classical laminated beam theory is employed to obtain the force-deformation relationships. The analysis provides explicit solutions to the structural response of the actuator, including strain and curvature of actuator's midplane. A numerical example for a cantilever box beam with uniform square cross-section subjected to a transverse concentrated load is presented. Results demonstrate that significant changes occur in the actuator's responses during phase transformation due to the strain recovery.