Numerically Implemented Constitutive Model for SMA Applications Experiencing General Loads Resulting in Plastic Deformation and Large Rotations

As active structures become more prominent, the use of more capable numerical modeling has gained importance as an aid to the design process. The need to accurately account for the response of Shape Memory Alloys (SMAs) under complex loading paths has become increasingly important. Such paths are general in a stress-temperature space and may induce irreversible deformation (plasticity). In addition, the structural utilization of active SMA components often includes large deformations, specifically large rotations. This is especially important in beam bending and torsional applications. This work proposes a new method for implementing a phenomenological SMA model originally formulated using small strains into a numerical framework which preserves objectivity given large rigid body rotations. The implementation is shown to be straightforward, and example analyses are performed which demonstrate the usefulness of this capability. An extension of the model to include the generation of plastic strains is also discussed. Alterations to the numerical algorithms are addressed which allow the analysis of simultaneous transformation and yielding. Additional analyses are performed on structural members undergoing transformation and yielding while at the same time moving through large rotations.