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Variational modeling of shape memory alloys – an overview

  • Klaus Hackl , Philipp Junker and Rainer Heinen
Published/Copyright: June 11, 2013
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 102 Issue 6

Abstract

Shape memory alloys can be described in a uniform way relying on energetic considerations only. We present micromechanically motivated models for single and polycrystals. The approach studied here is based on energy minimization and includes hysteretic effects via a simple dissipation ansatz. It is capable of reproducing important aspects of the material behavior such as pseudoelasticity and pseudoplasticity. The influence of anisotropies in the crystalline texture as well as in the elastic constants of the austenite and the martensitic variants is also discussed. Furthermore, regularization is applied in order to receive localized but still mesh independent results for phase distributions in a finite element implementation. The entire presentation emphasizes the usage of variational methods leading to the notion of relaxed potentials. Interrelations to various other applications of these concepts will be highlighted.

Keywords: Shape memory alloys; Micromechanics; Phase transformation; Variational calculus
* Correspondence address, Prof. Dr. rer. nat. Klaus Hackl Insitute of Mechanics, Ruhr-University of Bochum D-44780 Bochum, Germany Tel.: +49 234 3225729 Fax: +49 234 3214154 E-mail:

Dedicated to Prof. F. D. Fischer on the occasion of his 70th birthday

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Received: 2010-11-17
Accepted: 2011-4-6
Published Online: 2013-06-11
Published in Print: 2011-06-01

© 2011, Carl Hanser Verlag, München

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https://doi.org/10.3139/146.110527
Keywords for this article
Shape memory alloys; Micromechanics; Phase transformation; Variational calculus

Articles in the same Issue

  1. Original Contributions
  2. Microstructure and adhesion of as-deposited and annealed Cu/Ti films on polyimide
  3. On the origin of inhomogeneous stress and strain distributions in single-crystalline metallic nanoparticles
  4. Contents
  5. Contents
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  10. An excursion into the design space of biomimetic architectured biphasic actuators
  11. Strategies for fracture toughness, strength and reliability optimisation of ceramic-ceramic laminates
  12. Fracture statistics of brittle materials at micro- and nano-scales
  13. Martensitic phase transformations of nanocrystalline NiTi shape memory alloys processed by repeated cold rolling
  14. Variational modeling of shape memory alloys – an overview
  15. Phase-field approach to martensitic phase transformations: Effect of martensite–martensite interface energy
  16. Modelling of diffusive and massive phase transformations in binary systems – thick interface parametric model
  17. On the strength of grain and phase boundaries in ferritic-martensitic dual-phase steels
  18. A micro-level strain analysis of a high-strength dual-phase steel
  19. Thermodynamic description of niobium-rich γ-TiAl alloys
  20. Phase transition and ordering behavior of ternary Ti–Al–Mo alloys using in-situ neutron diffraction
  21. Microstructure evolution and mechanical properties of an intermetallic Ti-43.5Al-4Nb-1Mo-0.1B alloy after ageing below the eutectoid temperature
  22. Investigation of Cu precipitation in bcc-Fe – Comparison of numerical analysis with experiment
  23. Modeling interfacial effects on the thermal conduction behavior of short fiber reinforced composites
  24. Electronic origin of structure and mechanical properties in Y and Nb alloyed Ti–Al–N thin films
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