Semi-analytical Model for Superelastic Behavior of Twisted Shape Memory Alloy Microfilament Yarns

Manufacturing improvements have enabled the integration of shape memory alloys (SMA) into novel form factors to offer tailored solutions to engineering applications. Of these form factors, multifunctional twisted SMA microfilament yarns offer tailorable superelastic behavior, improved actuation displacements, and increased flexibility for integration within textiles for medical devices, defense structures, and wearable technologies. However, the lack of understanding of the underlying physics of twisted SMA yarns limits the potential in functionalized SMA textiles. This paper develops a semi-analytical model of the micro-scale mechanics of superelastic SMA-twisted yarns to predict their macroscopic mechanical behavior. Using traditional yarn models redefined within SMA constitutive equations, the evolution of material phases of the microfilaments within the mesoscale yarn element is tracked to the predicted macroscale yarn force. Through validation, the functional dependence of the yarn response, including effective modulus and phase transition dynamics, on twist is predicted by the model. The model fills a knowledge gap necessary for manufacturing SMA yarns with desired mechanical characteristics, limiting application strains to avoid failure, and achieving consistent cycled behavior. The model provides a framework for modeling the shape memory effect in SMA microfilament yarns and establishes an understanding of SMA yarns for implementation within textile models.