A robust model of pseudoelasticity in shape memory alloys

SUMMARY A model of pseudoelasticity in shape memory alloys is developed within the incremental energy minimization framework. Three constitutive functions are involved: the Helmholtz free energy and rate‐independent dissipation that enter incrementally the minimized energy function, and the constrai...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2013-02, Vol.93 (7), p.747-769
Main Authors: Stupkiewicz, S., Petryk, H.
Format: Article
Language:English
Subjects:
augmented Lagrangian method
Dissipation
Energy conservation
energy methods
finite element method
Mathematical analysis
Mathematical models
phase transformation
Pseudoelasticity
Shape memory alloys
shape memory alloys (SMA)
Strain
Transformations
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Summary:SUMMARY A model of pseudoelasticity in shape memory alloys is developed within the incremental energy minimization framework. Three constitutive functions are involved: the Helmholtz free energy and rate‐independent dissipation that enter incrementally the minimized energy function, and the constraint function that defines the limit transformation strains. The proposed implementation is based on a unified augmented Lagrangian treatment of both the constitutive constraints and nonsmooth dissipation function. A methodology for easy reformulation of the model from the small‐strain to finite‐deformation regime is presented. Finite element computations demonstrate robustness of the finite‐strain version of the model and illustrate the effects of tension–compression asymmetry and transversal isotropy of the surface of limit transformation strains. Copyright © 2012 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4405