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Shape Memory Alloys (SMAs) has been widely aware of working as actuators foractive/smart morphing structures in the engineering industry. Because of thehigh actuation energy density of SMAs, compared to other active materials,structures integrated with SMA-based actuators has high advantage in terms oftrade-offs between overall structure weight, integrity and functionality. Themajority of available constitutive models for SMAs are developed within theinfinitesimal strain regime. However, it was reported that particular SMAs cangenerate transformation strains nearly up to 8%-10%, for which the adoptedinfinitesimal strain assumption is no longer appropriate. Furthermore, industryapplications may require SMA actuators undergo large rotation deformation atwork. Combining the above two facts, a constitutive model for SMAs developed ona finite deformation framework is required. A three-dimensional constitutivemodel for SMAs considering large strains with large rotations is proposed inthis work. This model utilizes the logarithmic strain as a finite strainmeasure for large deformation analysis so that its rate form hypo-elasticconstitutive relation can be consistently integrated to deliver a free energybased hyper-elastic constitutive relation. The martensitic volume fraction andthe second-order transformation strain tensor are chosen as the internal statevariables to characterize the inelastic response exhibited by polycrystallineSMAs. The presented formulation and its numerical implementation scheme can beextended in future work for the incorporation of other inelastic phenomena suchas transformation-induced plasticity, viscoplasticity and creep under largedeformations.

A Three-dimensional Constitutive Model for Polycrystalline Shape Memory Alloys Under Large Strains Combined With Large Rotations