  Shape Memory Alloys (SMAs) are materials with the ability to recover
apparently permanent deformation under specific thermomechanical loading. The
majority of constitutive models for SMAs are developed based on the
infinitesimal strain theory. However, such assumption may not be proper in the
presence of geometric discontinuities, such as cracks, and repeated cycling
loading that has been reported to induce irrecoverable strains up to 20% due to
transformation induced plasticity. In addition to finite strains, SMA-based
devices may also undergo large rotations. Thus, it is indispensable to develop
a constitutive model based on the finite strain to provide accurate predictions
of these actuators response. A three-dimensional phenomenological constitutive
model for SMAs considering finite strains and finite rotations is proposed in
this work. This model utilizes the logarithmic strain as the strain measure
that is the strain measure whose logarithmic rate in a corotating material
frame is equal to the rate of deformation tensor. In the proposed model, the
martensitic volume fraction and the second-order logarithmic transformation
strain tensor are chosen as the internal state variables associated with the
inelastic transformation process. Numerical simulations considering basic SMAs
component geometries such as a bar, a beam, and a torque tube are performed to
test the capabilities of the proposed model under both mechanically and
thermally induced phase transformation. The presented model formulation will be
extended in future work for the incorporation of transformation-induced
plasticity.
