In this article a finite element implementation of a multivariant constitutive model of shape memory alloys for a mono-dimensional element is presented. The model has been implemented by writing the kinetic law and the equilibrium equation in the rate form and integrating this equation along the thermomechanical load path. The implemented model allows to simulate both the operation in isothermal condition, in full or partial pseudoelastic recover and the behavior of shape memory alloy’s wire in mixed thermal and mechanical load application such as in cyclic activations of a wire against a structure. The developed model is suitable for integration in structural finite element program allowing to simulate the action of SMA wires in integrated in complex structure. A number of numerical cases for the developed model are showed in order to verify the ability to reproduce expected typical SMA behaviors.
Auricchio, F.1995. Shape-Memory Alloys: Applications, Micromechanics, Macromodelling and Numerical Simulations, PhD Thesis, University of California , Berkeley.
2.
Auricchio, F. and Sacco, E.1999. ‘‘A Temperature-dependent Beam for Shape-Memory Alloys: Constitutive Modelling, Finite-element Implementation and Numerical Simulations,’’ Computer Methods in Applied Mechanics and Engineering, 174:171-190.
3.
Auricchio, F., Fugazza, D. and Des Roches, R.2007. ‘‘A 1D Rate-dependent Viscous Constitutive Model for Superelastic Shape-Memory Alloys: Formulation and Comparison with Experimental Data,’’Smart Materials and Structures , 16:S39-S50.
4.
Auricchio, F., Fugazza, D. and Des Roches, R.2008. ‘‘Rate-dependent Thermo-mechanical Modelling of Superelastic Shape-memory Alloys for Seismic Applications,’’Journal of Intelligent Material Systems and Structures, 19:47-61.
5.
Barbarino, S., Ameduri, S., Lecce, L. and Concilio, A.2009. ‘‘Wing Shape Control Through an SMA-Based Device,’’Journal of Intelligent Material Systems and Structures, 20:283.
6.
Bekker, A. and Brinson, L.C.1998. ‘‘Phase Diagram Based Description of the Hysteresis Behavior of Shape Memory Alloys,’’ Acta Materialia , 46:3649-3665.
7.
Brinson, L.C.1993. ‘‘One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable,’’ Journal of Intelligent Material Systems and Structures, 4:229-242.
8.
Brinson, L.C. and Huang, M.S.1996. ‘‘Simplifications and Comparisons of Shape Memory Alloy Constitutive Models,’’ Journal of Intelligent Material Systems and Structures, 7:108-114.
9.
Brinson, L.C., Huang, M.S., Noller, C. and Brandt, W.1997. ‘‘Analysis of Controlled Beam Deflection Using SMA Wires,’’ Journal of Intelligent Material Systems and Structures, 8:12-25.
10.
Brinson, L.C. and Lammering, R.1993. ‘‘Finite Element Analysis of the Behavior of Shape Memory Alloys and Their Applications,’’ International Journal of Solids and Structures, 30:3261-3280.
11.
Chung, J.-H., Heo, J.-S. and Lee, J.-J.2007. ‘‘Implementation Strategy for the Dual Transformation Region in the Brinson SMA Constitutive Model,’’Smart Materials and Structures, 16(1):N1-N5(1).
12.
Crisfield, M.A.2003. Non-linear Finite Element Analysis of Solids and Structures , Vol 1, John Wiley & Sons , New York.
13.
Daghia, F., Inman, D.J., Ubertini, F. and Viola, E.2008. ‘‘Shape Memory Alloy Hybrid Composite Plates for Shape and Stiffness Control,’’ Journal of Intelligent Material Systems and Structures, 19:609-619.
14.
Gao, X., Qiao, R. and Brinson, L.C.2007. ‘‘Phase Diagram Kinetics for Shape Memory Alloys: A Robust Finite Element Implementation,’’ Smart Materials and Structures, 16:2102-2115.
15.
Ghomshei, M.M., Khajepour, A., Tabandeh, N. and Behdinan, K.2001. ‘‘Finite Element Modeling of Shape Memory Alloy Composite Actuators: Theory and Experiment,’’ Journal of Intelligent Material Systems And Structures, 12:761-773.
16.
Ikeda, T.2008. ‘‘Constitutive Model of Shape Memory Alloys for Asymmetric Quasiplastic Behavior,’’ Journal of Intelligent Material Systems And Structures, 19:533-540.
17.
Ivshin, Y. and Pence, T.J.1994a. ‘‘A Constitutive Model for Hysteretic Phase Transition Behaviour,’’ International Journal of Engineering Science, 32:681-704.
18.
Ivshin, Y. and Pence, T.J.1994b. ‘‘A Thermomechanical Model for a one Variant Shape Memory Material,’’ Journal of Intelligent Materials Systems and Structures, 1:207-234.
19.
Liang, C. and Rogers, C.A.1990. ‘‘One-Dimensional Thermomechanical Constitutive Relations For Shape Memory Materials,’’ Journal of Intelligent Material Systems and Structures, 1:207-243.
20.
Liang, C. and Rogers, C.A.1997. ‘‘Design of Shape Memory Alloys Actuators ,’’ Journal of Intelligent Material Systems and Structures, 8:303-313.
21.
Manzo, J. and Garcia, E.2009. ‘‘Methodology for Design of an Active Rigidity Joint,’’Journal of Intelligent Material Systems and Structures, 20:311.
22.
Masuda, A., Panahandehb, M. and Aurrichio, F.1998. ‘‘A Finite-strain Finite Element Model for the Pseudoelastic Behavior of Shape Memory Alloys,’’ Computer Methods in Applied Mechanics and Engineering, 148:23-37.
23.
Paradis, A., Terriault, P., Brailovski, V. and Torra, V.2008. ‘‘On the Partial Recovery of Residual Strain Accumulated During an Interrupted Cyclic Loading of NiTi Shape Memory Alloys,’’Smart Materials and Structures, 17:065027.
24.
Sreekumar, M., Nagarajan, T. and Singaperumal, M.2008. ‘‘Experimental Investigations of the Large Deflection Capabilities of a Compliant Parallel Mechanism Actuated by Shape Memory Alloy Wires,’’Smart Materials and Structures , 17:065025.
25.
Sato, Y. and Tanaka, K.1988. ‘‘Estimation of Energy Dissipation in Alloys Due to Stress-Induced Martensitic Transformation’’Res Mechanica, 23: 381-393.
26.
Tanaka, K. and Nagaki, S.1982. ‘‘A Thermomechanical Description of Material with Internal Variables in the Process of Phase Transitions, ’’ Ingenieur Archive, 51:287-299.
