Modeling of the Thermomechanical Response of Active Laminates with SMA Strips Using the Layerwise Finite Element Method

Abstract

A study on the effective thermomechanical response of a composite laminate with shape memory alloy (SMA) layers based on the implementation of the layerwise laminate theory in the finite element method is carried out in this paper. The SMA thermomechanical constitutive response is based on a thermomechanical model recently developed by Boyd and Lagoudas. The numerical implementation of the constitutive model is based on a return mapping integration algorithm which is employed in studying the SMA response characteristics in the composite laminate under thermal loading. In modeling the laminate, a displacement based finite element approach is used in conjunction with the layerwise laminate theory of Reddy, incorporating piecewise continuous distribution of transverse strains through the thickness. As an illustrative example, the deformations caused by two prestrained SMA strips placed symmetric to the mid-plane of an elastic plate, when thermally activated are studied. The top SMA strip starts transforming from the martensitic into the austenitic state upon actuation through resistive heating, simultaneously recovering the prestrain, thus causing the laminate to bend. A parametric study investigating plane strain and generalized plane strain is carried out, and the accuracy of the results is compared with the commercial finite element code ABAQUS. The main feature of the presented methodology is an accurate evaluation of actuation stresses in the SMA strips, efficiently combining the layerwise geometry with the finite element method.

Get full access to this article

View all access options for this article.

References

Baz, A. and T. Chen . 1992. "Performance of Nitinol-Reinforced Drive Shafts", Smart Structures and Intelligent Systems, SPIE, 1917:791-791.

Baz, A. , J. Ro , M. Mutua and J. Gilheany . 1992. "Active Buckling Control of Nitinol-Reinforced Composite Beams", Proceedings of the ADPA/ AIAA/ASME/SPIE Conference on Active Materials and Adaptive Structures, Alexandria, VA, pp. 167-176.

Baz, A. , J. Ro , S. Poh and J. Gilheany . 1993. "Control of Smart Traversing Beam", Proceedings of the ADPA/AIAA/ASME/SPIE Conference on Active Materials and Adaptive Structures, Alexandria, VA, pp. 167-176.

Bhattacharyya, A. , D. C. Lagoudas , Y. Wang and V. K. Kinra . 1995. "On the Role of Thermoelectric Heat Transfer in the Design of SMA Actuators: Theroretical Modeling and Experiment", Smart Materials and Structures, 4:252-263.

Boyd, J. G. and D. C. Lagoudas . 1994. "Thermomechanical Response of Shape Memory Composites", Journal of Intelligent Materials and Structures, 5:333-346.

Boyd, J. G. and D. C. Lagoudas . 1996. "A Thermodynamic Constitutive Model for the Shape Memory Materials. Part I. The Monolithic Shape Memory Alloys", International Journal of Plasticity, 12(86):805-842.

Brand, W. , C. Boller , M. S. Huang and L. C. Brinson . 1994. "Introducing the Constitutive Behavior of Shape Memory Alloys into Adaptive Engineering Structures", Proceedings of the ASME Winter Annual Meeting: Symposium on the Mechanics of Phase Transformations and Shape Memory Alloys, Chicago, IL, p. 275-275.

Epps, J. and R. Chandra . 1995. "Shape Memory Alloy Actuation for Active Tuning of Composite Beams", Smart Structures and Materials, SPIE, 2443:76-88.

Giurgiutiu, V. , Z. Chaudhry and C. A. Rogers . 1994. "The Analysis of Power Delivery Capability of Induced Strain Actuators for Dynamic Applications", Proceedings of the Second International Conference on Intelligent Materials, C. A. Rogers and G. C. Wallace , eds., Colonial Williamsburg, VA, pp. 565-576.

10.

Hebda, D. A. and S. R. White . 1995. "Structural Behavior of SMA Composite Beams", Adaptive Material Systems, ASME, AMD-Vol. 206/ MD-Vol. 58, pp. 111-119.

11.

Hebda, D. A. , M. E. Whitlock , J. B. Ditman and S. R. White . 1995. "Manufacturing of Adaptive Graphite Epoxy Structures with Embedded Nitinol Wires", Journal of Intelligent Material Systems and Structures, 6:220-228.

12.

Lagoudas, D. C. and Z. Bo . 1994. "The Cylindrical Bending of Composites Plated with Piezoelectric and SMA Layers", Smart Materials and Structures, 3:309-317.

13.

Lagoudas, D. C. and I. G. Tadjbakhsh . 1992. "Active Flexible Rods with Embedded SMA Fibers", Smart Materials and Structures, 1: 162-167.

14.

Lagoudas, D. C. , J. G. Boyd and Z. Bo . 1994. "Micromechanics of Active Composites with SMA Fibers", ASME Journal of Material Science and Technology, 1 16(3):337-347.

15.

Lagoudas, D. C. , Z. Bo and M. A. Qidwai . 1996. "A Unified Thermodynamic Constitutive Model for SMA and Finite Element Analysis of Active Metal Matrix Composites", Mechanics of Composite Materials and Structures, 3:153-179.

16.

Lalande, F. , Z. Chaudhry and C. A. Rogers . 1994. "Comparison of Different Impedance-Based Models for Out-of-Phase Actuation of Actuators Bonded on Ring Structures", Proceedings of the Second International Conference on Intelligent Materials, C. A. Rogers and G. C. Wallace , eds., Colonial Williamsburg, VA, pp. 771-782.

17.

Liang, C. and C. A. Rogers . 1992. "A Fully Coupled Acoustic Analysis of Curved PVDF Acoustic Actuators for Active Sound Attenuation", Proceedings of the Conference on Adaptive and Sensory Materials and Their Applications, C. A. Rogers and R. C. Rogers , eds., Blacksburg, VA, pp. 765-779.

18.

Liang, C. , F. Sun and C. A. Rogers . 1994. "An Investigation of the Energy Consumption and Conversion of Piezoelectric Actuators Integrated in Active Structures," Proceedings of the Second International Conference on Intelligent Materials, C. A. Rogers and G. C. Wallace , eds., Colonial Williamsburg, VA, pp. 828-845.

19.

Liang, C. , F. Davidson , L. M. Schetky and F. K. Straub . 1996. "Applications of Torsional Shape Memory Alloy Actuators for Active Rotor Blade Control-Opportunities and Limitations", SPIE, 2717:91-100.

20.

Lin, M. W. and C. A. Rogers . 1994. "Analysis of a Beam Structure with Induced Strain Actuators Based on an Approximated Linear Shear Stress Field", Proceedings of the Conference on Adaptive and Sensory Materials and Their Applications, C. A. Rogers and R. C. Rogers , eds., Blacksburg, VA, pp. 363-375.

21.

Lin, M. W. , A. O. Abatan and C. A. Rogers . 1994. "Application of Commercial Finite Element Codes for the Analysis of Induced Strain Actuated Structures", Proceedings of the Second International Conference on Intelligent Materials, C. A. Rogers and G. C. Wallace . eds., Colonial Williamsburg, VA, pp. 846-855.

22.

Mau, S. T. 1973. "A Refined Laminate Plate Theory", Journal of Applied Mechanics, 40:606-607.

23.

Mitchell, J. A. and J. N. Reddy . 1995. "A Refined Hybrid Plate Theory for Composite Laminates with Piezoelectric Laminae", International Journal of Solids and Structures, 32:2345-2367.

24.

Ortiz, M. and J. C. Simo . 1986. "An Analysis of a New Class of Integration Algorithms for Elastoplastic Constitutive Relations", International Journalfor Numerical Methods in Engineering, 23:353-366.

25.

Paine, J. S. N. and C. A. Rogers . 1994. "Shape Memory Alloys for Damage Resistant Composite Structures", Active Materials and Smart Structures, SPIE, 2427:358-371.

26.

Reddy, J. N. 1969. "On the Generalization of Displacement-Based Laminate Theories", Applied Mechanics Review, 42(1l)(Part 2):S213-S222.

27.

Reddy, J. N. 1987. "A Generalization of Two-Dimensional Theories of Laminate Composite Plates", Commun. Appl. Numer. Methods, 3:173-180.

28.

Reddy, J. N. 1993. An Introduction to the Finite Element Method New York: McGraw Hill Inc.

29.

Robbins, D. H. and J. N. Reddy . 1991. "Analysis of Piezoelectrically Activated Beams Using a Layerwise Displacement Theory", Computers and Structures, 41:265-279.

30.

Robbins, D. H. and J. N. Reddy . 1993. "Modeling of Thick Composites Using a Layerwise Laminate Theory", International Journalfor Numerical Methods in Engineering, 36:655-677.

31.

Rogers, C. A. , C. Liang and J. Jia . 1989a. "Behavior of Shape Memory Alloy Reinforced Composite Plates. Part I: Model Formulation and Control Concepts", AIAA, p. 2011-2011.

32.

Rogers, C. A. , C. Liang and J. Jia . 1989b. "Behavior of Shape Memory Alloy Reinforced Composite Plates. Part II: Results", AIAA, p. 1504-1504.

33.

Srinivas, S. 1973. "Refined Analysis of Composite Plates,", Journal of Sound and Vibrations, 30:495-507.

34.

Srinivasan, A. V. , D. G. Cutts and L. M. Schetky . 1991. "Thermal and Mechanical Considerations in Using Shape Memory Alloys to Control Vibrations in Flexible Structures", Metallurgical Transactions A, 22A: 623-627.

35.

Sun, F. P. , Z. Chaudhry , C. A. Liang and C. A. Rogers . 1994. "Truss Structure Identification Using PZT Sensor Actuator", Proceedings of the Second International Conference on Intelligent Materials, C. A. Rogers and G. C. Wallace , eds., Colonial Williamsburg, VA, pp. 1210-1222.

36.

Xu, G. , D. C. Lagoudas , J. J. Wen and D. Hughes . 1995. "Thermo-Electro-Mechanical Modeling and Structural Response of a Flexible Beam with Extemal SMA Actuators", Smart Structures and Materials 1995, Proceedings of the 1995 SPIE Arorth American Conference on Smart Structures and Materials, SPIE, San Diego, CA, 2441:503-510.

37.

Yu, Y. Y. 1959. "A New Theory of Elastic Sandwich Plates-One Dimensional Case", Journal of Applied Mechanics, 26:415-421.