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Theoretical Analysis of a Functionally Graded Shape Memory Alloy Beam under Pure Bending

Lijun Xue1, Guansuo Dui1,2, Bingfei Liu3

Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China.
Corresponding author.
Tel.: +1-86-1051688437; fax: +1-86-1051682094. E-mail:
Airport College, Civil Aviation University of China, Tianjin 300300, China.

Computer Modeling in Engineering & Sciences 2013, 93(1), 1-16.


The Functionally Graded Shape Memory Alloy (FG-SMA) is a new kind of functional materials which possesses the excellent properties of both Shape Memory Alloy (SMA) and Functionally Graded Material (FGM). A macro constitutive model of FG-SMA is established by using the theory of the mechanics of composites and the existing SMA model. With this macro constitutive model, the mechanical behavior of a FG-SMA beam composed by elastic material A and SMA subjected to pure bending is investigated. The loading processes including elastic process and phase transformation process are discussed in detail and the analytical solutions are obtained. What is more, a new layered method for establishing the finite element model of the FG-SMA beam is provided. The theoretical results show a good agreement with the experiment data, which indicates that the macro constitutive model and the finite element method provided here are valid. At last, the stress distribution on the cross section, the position of the neutral axis and the curvature-bending moment relation are discussed through numerical results, respectively. The obtained results demonstrate several interesting features of this new material, which may have potential applications in the future. This research can provide a base for the design and in-depth investigation of FG-SMA material.


Cite This Article

Xue, L., Dui, G., Liu, B. (2013). Theoretical Analysis of a Functionally Graded Shape Memory Alloy Beam under Pure Bending. CMES-Computer Modeling in Engineering & Sciences, 93(1), 1–16.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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