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February 8, 2026International Journal for Numerical Methods in Engineering0 citationsOpen Access

Variational Thermomechanically Coupled Shape Memory Alloy Material Model and Optimization of Shape Memory Alloy Based Out‐of‐Plane Bistable Microactuator

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MSMuhammad Babar ShamimHGHauke GoldbeckSWS. Wulfinghoff

Key Points

  • To develop a thermomechanically coupled material model for shape memory alloys that predicts their behavior in actuation applications.
  • Developed a fully thermomechanically coupled model for SMAs using the Generalized Standard Material framework.
  • Employed a rate potential to derive governing equations like momentum balance and energy balance.
  • Integrated a potential-based line search with a Newton-Raphson scheme for solution optimization.
  • Applied the model to design an out-of-plane bistable microactuator with two SMA microbridges.
  • Successfully predicted shape memory effect, superelasticity, and martensite reorientation in SMAs.
  • Demonstrated the bistable behavior of the actuator, capable of switching states under thermomechanical loading.
  • Highlighted the efficiency and accuracy of the model in simulating the complex responses of SMA devices.

Abstract

ABSTRACT This work presents a fully thermomechanically coupled material model for shape memory alloys (SMAs), capable of predicting shape memory effect, superelasticity, stress and strain recovery, and martensite reorientation. Formulated within the Generalized Standard Material (GSM) framework, the model employs a rate potential, whose variations yield the governing equations, including linear momentum balance, energy balance, and evolution of internal variables. A potential‐based line search method integrated with a Newton–Raphson scheme enhances the robustness and convergence of the solution algorithm. Extending the Sedlák 14 model's energy and dissipation formulations, we apply the proposed framework to an SMA‐based out‐of‐plane bistable microactuator design. The actuator features two antagonistically coupled SMA microbridges and exhibits bistable behavior, snapping between stable states under thermomechanical loading and using constrained recovery forces to perform work. Results demonstrate the model's efficiency and accuracy in capturing the complex thermomechanical response of SMA devices, highlighting its potential for advanced bistable actuator design.

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Cite This Study

Shamim et al. (2026) studied this question.

synapsesocial.com/papers/698827f00fc35cd7a884705ehttps://doi.org/10.1002/nme.70263
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