Constitutive model of shape memory alloys for unidirectional loading considering inner hysteresis loops

A specimen-based macroscopic constitutive model of shape memory alloys for unidirectional loading, which is simple yet accurate and has a physical background, was derived from a grain-based microscopic model. To consider the inner hysteresis loops of a stress–strain–temperature relationship, a new inner loop model called the shift and skip model was proposed. This model is based on microscopic aspects and includes the memory effect of deformation history. Stress–strain relationships were simulated for some representative strain cycles. Numerical results showed that the proposed simple model could capture corresponding experimental results accurately enough to be applied for smart structural design. Comparison with major specimen-based macroscopic models was also discussed, under a unifying approach based on the driving energy and required transformation energy pair.