We analyze wave propagation in a semi-infinite shape memory alloy (SMA) bar under a rectangular impulsive loading. Different trilinear up–down–up nominal stress–strain curves for loading and unloading processes are adopted to complete the dynamical system. The chord criterion (equivalent to maximally dissipative kinetics) is employed to single out the unique solution for the impact problem. The interactions among discontinuities (loading/unloading elastic shock waves and phase boundaries) can yield some complicated wave structure. In particular, it is found that the encounter of the unloading elastic shock wave and the loading phase boundary can yield three different wave patterns depending on the level of impact stress, which are different from those for a hardening response studied in the literature. Solutions in the whole temporal and spatial domain are obtained, which reveal interesting wave structures induced by two different levels of impact. Phase transformation regions and tension/compression regions are also determined. The results also suggest that the SMAs can be used for impact-protection purpose effectively.
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October 2016
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Wave Propagation in a Shape Memory Alloy Bar Under an Impulsive Loading
Pingping Zhu,
Pingping Zhu
Department of Mathematics,
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: ppzhu2-c@my.cityu.edu.hk
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: ppzhu2-c@my.cityu.edu.hk
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Hui-Hui Dai
Hui-Hui Dai
Department of Mathematics,
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: mahhdai@cityu.edu.hk
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: mahhdai@cityu.edu.hk
Search for other works by this author on:
Pingping Zhu
Department of Mathematics,
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: ppzhu2-c@my.cityu.edu.hk
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: ppzhu2-c@my.cityu.edu.hk
Hui-Hui Dai
Department of Mathematics,
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: mahhdai@cityu.edu.hk
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: mahhdai@cityu.edu.hk
1Corresponding author.
Manuscript received June 6, 2016; final manuscript received July 6, 2016; published online July 27, 2016. Assoc. Editor: Daining Fang.
J. Appl. Mech. Oct 2016, 83(10): 104502 (6 pages)
Published Online: July 27, 2016
Article history
Received:
June 6, 2016
Revised:
July 6, 2016
Citation
Zhu, P., and Dai, H. (July 27, 2016). "Wave Propagation in a Shape Memory Alloy Bar Under an Impulsive Loading." ASME. J. Appl. Mech. October 2016; 83(10): 104502. https://doi.org/10.1115/1.4034115
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