An analytical study of the instability of a superelastic shape memory alloy cylinder subject to practical boundary conditions

Smart Materials and Structures

Volumn 18, Issue 2, 2009, Pages

  Dai, Hui Hui ^a   Wang, Jiong ^a   Chen, Zhen ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b University of Missouri   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC EXPANSIONS; ASYMPTOTIC SOLUTIONS; AXI-SYMMETRICAL; BOUNDARY-VALUE PROBLEMS; COMPLICATED SYSTEMS; COMPRESSIBLE HYPERELASTIC MATERIALS; END CONDITIONS; FIRST ORDERS; GLOBAL BIFURCATIONS; KEY FEATURES; NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS; NON-LINEAR PDES; NORMAL FORMS; PHASE-PLANE ANALYSIS; PRACTICAL BOUNDARY CONDITIONS; STRAIN ENERGY FUNCTIONS; SUPERELASTIC SHAPE MEMORY ALLOYS; THREE-DIMENSIONAL SETTINGS; TRANSITION PROBLEMS;

AIRCRAFT ENGINES; ALLOYS; ASYMPTOTIC ANALYSIS; BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; CIRCULAR CYLINDERS; DYNAMICAL SYSTEMS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; STRESS-STRAIN CURVES; THREE DIMENSIONAL;

PHASE TRANSITIONS;

EID: 65249144497     PISSN: 09641726     EISSN: 1361665X     Source Type: Journal    
DOI: 10.1088/0964-1726/18/2/024007     Document Type: Article

References (17)

1. Abeyaratne R, Bhattacharya K and Knowles J K 2001 Strain-energy functions with multiple local minima: modeling phase transformations using finite thermoelasticity Nonlinear Elasticity: Theory and Applications ed Y Fu and R Ogden (Cambridge: Cambridge University Press) pp 433-90
2. Ball J M and James R D 1992 Proposed experimental tests of a theory of fine microstructure and the two well problem Phil. Trans. R. Soc. A 338 389-450
3. Cai Z X and Dai H H 2006 Phase transitions in a slender cylinder composed of an incompressible elastic material. II. Analytical solutions for two boundary-value problems Proc. R. Soc. A 462 419-38
4. Chang B C, Shaw J A and Iadicola M A 2006 Thermodynamics of shape memory alloy wire: modeling, experiments, and application Contin. Mech. Thermodyn. 18 83-118 (Pubitemid 44075780)
5. Dai H H and Cai Z X 2006 Phase transitions in a slender cylinder composed of an incompressible elastic material. I. Asymptotic model equation Proc. R. Soc. A 462 75-95
6. Dai H H and Fan X J 2004 Asymptotically approximate model equations for weakly nonlinear long waves in compressible elastic rods and their comparisons with other simplified model equations Math. Mech. Solids 9 61-79
7. Dai H H and Huo Y 2002 Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods Acta Mech. 157 97-112
8. Ericksen J L 1975 Equilibrium bars J. Elast. 5 191-201
9. Favier D, Liu Y, Orgeas L and Rio G 2001 Mechanical instability of NiTi in tension, compression and shear Proc. IUTAM Symp. on Mechanics of Martensitic Phase Transformation in Solids ed Q P Sun (Boston, MA: Kluwer-Academic) pp 205-12
10. Fu Y B and Ogden R W 1999 Nonlinear stability analysis of pre-stressed elastic bodies Contin. Mech. Thermodyn. 11 141-72 (Pubitemid 129494519)
11. Li Z Q and Sun Q P 2002 The initiation and growth of macroscopic martensite band in nanograined NiTi microtube under tension Int. J. Plast. 18 1481-98
12. Shaw J A and Kyriakides S 1995 Thermomechanical aspects of NiTi J. Mech. Phys. Solids 47 1243-81
13. Shaw J A and Kyriakides S 1997 On the nucleation and propagation of phase transformation fronts in a NiTi alloy Acta Mater. 45 683-700 (Pubitemid 127415436)
14. Shaw J A and Kyriakides S 1998 Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension Int. J. Plast. 13 837-71
15. Sun Q P, Li Z Q and Tse K K 2000 On superelastic deformation of NiTi shape memory alloy micro-tubes and wires-band nucleation and propagation Proc. IUTAM Symp. on Smart Structures and Structure Systems ed U Gabbert and H s Tzou (Dordrecht: Kluwer-Academic) pp 1-8
16. Tong P, Lam C C and Sun Q P 2001 Phase transformation of thin wires in tension Proc. IUTAM Symp. on Mechanics of Martensitic Phase Transformation in Solids (Hong Kong, June 2001) ed Q P Sun (Boston, MA: Kluwer-Academic) pp 221-32
17. Tse K K and Sun Q P 2000 Some deformation features of polycrystalline superelastic NiTi shape memory alloy thin strips and wires under tension Key Eng. Mater. 177-180 455-60