A new mechanism-based phenomenological model, comprising linear and nonlinear springs and a nonlinear friction element, is presented for the pseudoelastic damping behavior of shape memory alloys. The use of a partial hyperbolic tangent friction element (a hybrid of an ideal and hyperbolic tangent friction element) is seen to increase accuracy in simulating experimental hysteresis behavior over earlier models. Comparisons are then made with existing models. Compared to the thermodynamic-based models, the present models have the benefit of not requiring calculation of austenite-martensite phase transformations. Unlike previously developed phenomenological models, the models presented herein have mechanical analogies that provide a strong physical basis, and clear relationships can be established between the unlocking of the friction element and the occurrence of phase transformation. These models are simpler and more intuitive than existing models.

1.
Hodgson
,
D. E.
, 1988, “
Using Shape Memory Alloys
,”
Shape Memory Applications, Inc.
2.
Thompson
,
P.
,
Balas
,
G. J.
, and
Leo
,
P. H.
, 1993, “
Pseudoelastic Hysteresis of Shape Memory Wires for Passive Structural Damping: Theory and Experiments
,”
Proc. SPIE
0277-786X,
2193
.
3.
Yiu
,
Y. C.
, and
Regelbrugge
,
M. E.
, 1995, “
Shape Memory Alloy Isolators for Vibration Suppression in Space Applications
,”
American Institute of Aeronautics and Astronautics
, AIAA-95–1120-CP.
4.
Witting
,
P. R.
, and
Cozzarelli
,
F. A.
, 1993, “
Design and Seismic Testing of Shape Memory Structural Dampers
,”
Proceedings of Damping ’93
, Paper No. ECC-1.
5.
Gandhi
,
F.
, and
Chapuis
,
G.
, 2002, “
Passive Damping Augmentation of a Vibrating Beam Using Pseudoelastic Shape Memory Alloy Wires
,”
J. Sound Vib.
0022-460X,
250
(
3
), pp.
519
539
.
6.
Tanaka
,
K.
, 1990, “
A Phenomenological Description on Thermomechanical Behavior of Shape Memory Alloys
,”
ASME J. Pressure Vessel Technol.
0094-9930,
112
, pp.
158
163
.
7.
Liang
,
C.
, and
Rogers
,
C. A.
, 1990, “
One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Alloys
,”
American Institute of Aeronautics and Astronautics
, AIAA-90–1027-CP.
8.
Brinson
,
L. C.
, 1993, “
One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation With Non-Constant Material Functions and Redefined Martensite Internal Variable
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
4
, pp.
229
242
.
9.
Boyd
,
J. G.
, and
Lagoudas
,
D. C.
, 1994, “
A Constitutive Model for Simultaneous Transformation and Reorientation in Shape Memory Materials
,”
Mechanics of Phase Transformations and Shape Memory Alloys
,
ASME AMD
189
∕PVP
292
.
10.
Shaw
,
J. A.
, and
Kyriakides
,
S.
, 1995, “
Thermomechanical Aspects of NiTi
,”
J. Mech. Phys. Solids
0022-5096,
43
(
8
), pp.
1243
1281
.
11.
Graesser
,
E. J.
, and
Cozzarelli
,
F. A.
, 1991, “
Shape Memory Alloys as New Materials for Aseismic Isolation
,”
J. Eng. Mech.
0733-9399,
117
(
11
), pp.
2590
2608
.
12.
Graesser
,
E. J.
, and
Cozzarelli
,
F. A.
, 1994, “
A Proposed Three Dimensional Model for Shape Memory Alloys
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
5
, pp.
78
88
.
13.
Graesser
,
E. J.
, and
Cozzarelli
,
F. A.
, 1991, “
Extension of a One-Dimensional Model of Hysteresis to Three Dimensions: Procedure and Verification
,”
High Temperature Constitutive Modeling: Theory and Application
,
ASME MD
26
∕AMD
121
,
A.
Freed
and
K.
Walker
, eds., pp.
365
381
.
14.
Graesser
,
E. J.
, and
Cozzarelli
,
F. A.
, 1993,
Full Cyclic Hysteresis of a Ni–Ti Shape Memory Alloy
,”
Proceedings of Damping ’93
, Vol.
2
, pp.
ECB
-1–
28
.
15.
Witting
,
P. R.
, and
Cozzarelli
,
F. A.
, 1994, “
Experimental Determination of Shape Memory Alloy Constitutive Model Parameters
,”
Proc. SPIE
0277-786X,
2427
, pp.
260
275
.
16.
Witting
,
P. R.
, 1994, “
Rate Sensitive Shape Memory Constitutive Model: Theory and Experimental Verification
,” Ph.D. dissertation, State University of New York at Buffalo, Buffalo, NY.
17.
Özdemir
,
H.
, 1976, “
Nonlinear Transient Dynamic Analysis of Yielding Structures
,” Ph.D. dissertation, University of California at Berkeley, Berkeley, CA.
18.
Gandhi
,
F.
, and
Wolons
,
D.
, 1999, “
Characterization of the Pseudoelastic Damping Behavior of Shape Memory Alloy Wires using Complex Modulus
,”
Smart Mater. Struct.
0964-1726,
8
, pp.
49
56
.
19.
Lazan
,
B. J.
, 1969,
Damping of Materials and Members in Structural Mechanics
,
1st ed.
Pergamon Press
,
Oxford
.
20.
Nashif
,
A. D.
,
Jones
,
D. I. G.
, and
Henderson
,
J. P.
, 1985,
Vibration Damping
,
Wiley
,
New York
.
21.
Flugge
,
W.
, 1967,
Viscoelasticity
,
Blaisdell, Waltham
.
22.
Gandhi
,
F.
, and
Chopra
,
I.
, 1994, “
An Analytical Model for a Nonlinear Elastomeric Lag Damper and Its Effect on Aeromechanical Stability in Hover
,”
J. Am. Helicopter Soc.
0002-8711,
39
(
4
), pp.
59
69
.
23.
Gandhi
,
F.
, and
Chopra
,
I.
, 1996, “
Analysis of Bearingless Main Rotor Aeroelasticity Using an Improved Time-Domain Nonlinear Elastomeric Damper Model
,”
J. Am. Helicopter Soc.
0002-8711,
41
(
3
), pp.
267
277
.
24.
Gandhi
,
F.
, and
Chopra
,
I.
, 1996, “
A Time-Domain Non-Linear Viscoelastic Damper Model
,”
Smart Mater. Struct.
0964-1726,
5
, pp.
517
528
.
25.
Kamath
,
G. M.
,
Wereley
,
N.
, and
Jolly
,
M.
, 1997, “
Analysis and Testing of a Model-Scale Magnetorheological Fluid Helicopter Lag Mode Damper
,”
Presented at the American Helicopter Society 53rd Annual Forum
, Virginia Beach, Virginia, 29 April–1 May.
26.
Kamath
,
G. M.
, and
Wereley
,
N. M.
, 1997, “
A Nonlinear Viscoelastic-Plastic Model for Electrorheological Fluids
,”
Smart Mater. Struct.
0964-1726,
6
, pp.
351
359
.
27.
Malovrh
,
B.
, and
Gandhi
,
F.
, 2001, “
Mechanism Based Phenomenological Models for the Pseudoelastic Hysteresis Behavior of Shape Memory Alloys
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
12
(
1
), pp.
21
30
.
28.
Wolons
,
D.
,
Gandhi
,
F.
, and
Malovrh
,
B.
, 1999, “
Experimental Investigation of the Pseudoelastic Hysteresis Damping Characteristics of Shape Memory Alloy Wires
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
10
, pp.
116
126
.
29.
Wolons
,
D. S.
, 1997, “
An Experimental Investigation of the Pseudoelastic Damping Characteristics of NiTi Shape Memory Alloy Wire
,” M.S. thesis, The Pennsylvania State University, Department of Aerospace Engineering.
You do not currently have access to this content.