ECCOMAS 2024

A Thermodynamic Approach to Modelling Shape Memory Alloys

  • Erdogan, Cem (Leibniz University Hannover)
  • Bode, Tobias (Leibniz University Hannover)
  • Junker, Philipp (Leibniz University Hannover)

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In this talk an efficient material model for shape memory alloys (SMA), a unique subset of "smart materials" within the broader category of "multifunctional materials", is presented. These materials are characterized by their significant sensing and actuation capabilities, which make them suitable for various high-tech applications in aerospace, medicine, automotive and robotics. A review of existing macroscopic models for SMAs reveals various theoretical approaches used to capture the complex behavior of SMAs. Among these, the model developed by Junker et al. is notable for its robust theoretical basis. Although this model relies mainly on thermal experiments, it has shown remarkable accuracy in predicting the mechanical behavior. Our model builds on Hamilton's principle and differs in several innovative features. It uses a rate-independent evolution of internal variables, which is essential for the accurate simulation of phase transformations in inherently diffusionless SMAs. Furthermore, we discuss algorithms that improve the robustness and convergence of the model when solving complex boundary value problems. A novel approach in our model is the parameterization of rotation matrices using Euler-Rodrigues parameters, which effectively solves the gimbal locking problem. The method for calculating the volume fractions of the crystallographic phases has also been refined by replacing the active set method with a more efficient penalty term and a sigmoid function. To demonstrate the functionality of the enhanced model, several application examples are presented. These selected examples illustrate how the model can successfully simulate complex and multi-layered load scenarios, highlighting the exceptional versatility and practical applicability of the model in solving real-world engineering problems.