4 June 1999 Mesomechanical modeling of shape memory effect
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Shape memory alloys (SMA) are well known materials. There is a lot of technical applications making use of their unique properties. Most of the significant applications are based on use of the thermomechancial properties. Growing number of those applications causes a need for an universal mathematical model with ability to describe all thermomechancial properties of SMA by relatively simple final set of constitutive equations that could be helpful for development of further sophisticated shape memory applications. Unfortunately, a lot of attention has been paid to metallurgical research of shape memory alloys in a few last decades and less attention was dedicated to shape memory modeling. Our model does not claim to be a universal model, but only one contribution to modeling of shape memory effect for binary SMA. The model is adapted for the most applied SMA -- nitinol and is based on the hypothesis that in the course of shape memory effect the distances of first atomic neighbors (Ni-Ti) remain nearly unchanged, whereas the distances of second neighbors (Ti-Ti and Ni-Ni) change substantially. Consequently, we consider some mechanical properties of Ni-substructure and Ti- substructure separately. The mechanical behavior of Ti- substructure is modeled as elastic whereas that of Ni- substructure as elasto-plastic. The resulting relatively simple differential constitutive equations express relationship among internal stress tensors, macroscopic stress tensors, macroscopic strain tensors and temperature.
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David Vokoun, David Vokoun, Vratislav Kafka, Vratislav Kafka, "Mesomechanical modeling of shape memory effect", Proc. SPIE 3667, Smart Structures and Materials 1999: Mathematics and Control in Smart Structures, (4 June 1999); doi: 10.1117/12.350109; https://doi.org/10.1117/12.350109

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