Thermomechanical Parameters Modelling of Spring Force Elements Made of Shape Memory Alloys

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Abstract
This study presents a phenomenological model for predicting the thermomechanical behaviour of spring-type actuators made of shape memory alloys (SMAs). The model incorporates the kinetics of martensite–austenite phase transitions as a function of temperature and applied stress. The primary innovation is the inclusion of a scalar internal variable that represents the evolution of the phase transformation within a phenomenological macroscopic model. This approach enables the deformation–force–temperature behaviour of SMA-based spring elements under cyclic loading to be accurately described. A set of constitutive equations was derived to describe reversible and residual strains, along with transformation start and finish conditions. Model parameters were calibrated using experimental data from VSP-1 and TN-1K SMA springs that were subjected to thermal cycling. The validation results show a high correlation between the theoretical predictions and the experimental data, with deviation margins of less than 6.5%. The model was then applied to designing and analysing thermosensitive actuator mechanisms for temperature control systems. This yielded accurate deformation–force characteristics, demonstrating low inertia and high repeatability. This approach enables the efficient prediction and improvement of the performance of SMA-based spring elements in actuators, making it relevant for adaptive systems in marine and aerospace applications.

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