Residual deformation of active structures with SMA actuators

Abstract In this paper, a three species thermomechanical constitutive model for Shape Memory Alloy (SMA) actuators, based on previous work by Boyd and Lagoudas (Proceedings of the 4th International Symposium on Plasticity and its Current Applications, Baltimore, MD, 19–23 July, 1993) is developed. The three species that contribute to the specific free energy of SMA are: self-accommodated martensite, detwinned martensite and austenite. The total martensitic volume fraction is decomposed into two parts: self-accommodated and detwinned martensite. The dissipation potentials, utilized for the evolution of the volume fractions of the two parts of martensite, are explicity given for 1-D. The concept of critical stress associated with detwinning of self-accommodated martensite, is introduced to incorporate the observed phenomenon during cooling of SMA actuators. The constitutive model described above is well suited for applications in active structures, because the maximum amount of the detwinned martensitic volume fraction is related to the current stress and temperature of the SMA actuator. This maximum amount of volume fraction can be reached during cooling in a constrained structural environment and is determined by the evolution of the internal variables. A prototype structural example, which is a flexible cantilever beam with an externally attached SMA actuator, is used to demonstrate the capability to predict the residual deformation and stress upon cooling.