Micro-Mechanical Model of a Composite Containing a Conservative Nonlinear Electro-Magneto-Thermo-Mechanical Material

Abstract

In this paper, we present an elasticity formulation using a concentric cylinders assemblage to investigate the response of a composite system containing a conservative nonlinear electro-magneto-thermo-mechanical (EMTM) material. The nonlinearity in the EMTM material is mathematically represented in the constitutive relations with terms coupling strain, electric/magnetic fields, temperature, and stress. These relations are representative of piezoelectric, electrostrictive, and magnetostrictive materials. The electric-magnetic-thermal field inside the composite material is assumed to be invariant with respect to position; this permits a closed form solution to be presented. The analytical model provides point wise stresses and strains in each constituent and is useful for evaluating possible locations for damage initiation and effective properties for the coupled material system. Parametric studies are presented to investigate the influence of constituents and actuator geometry on the material system's effective properties. Analytical results generated for a Terfenol-D composite indicate that nonlinear terms must be included to accurately characterize its response to large changes in stress or magnetic field strengths.

Get full access to this article

View all access options for this article.

References

Averill, R. and G.P. Carman. 1991. "Analytical and Numerical Modeling of Micromechanical Stress Variations in Continuous Fiber Reinforced Composites", IUTAM Symposium: Local Mechanics Concepts for Composite Material Systems.

Barrett, R. 1992. "Active Plate and Wing Research Using EDAP Elements ", Smart Materials and Structures, 1:214-226.

Benveniste, Y. and G.J. Dvorak. 1992. "Uniform Fields and Universal Relations in Piezoelectric Composites", Journal of the Mechanics and Physics of Solids, 40(6):1295-1312.

Brinson, L.C. 1993. "Constitutive Behavior of Shape Memory Alloys: One Dimensional Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable", Recent Advances in Adapative and Sensory Materials and Their Applications, Rogers and Rogers, eds., pp. 729-743.

Cao, W. , Q.M. Zhang and L.E. Cross. 1992. "Theoretical Study on the Static Performance of Piezoelectric Ceramic-Polymer Composites with 1-3 Connectivity", J. Appl. Phys., 72(12):5814-5821.

Carman, G.P. and M. Mitrovic. 1994. "Nonlinear Constitutive Relations for Magnetostrictive Materials", Proc. of the 2nd Int'l Conference on Intelligent Materials, July, pp. 265-278.

Chan, H.L. and J. Unsworth. 1989. "Simple Model for Piezoelectric Ceramic/Polymer 1-3 Composites Used in Ultrasonic Transducer Applications", IEEE Trans. Utrason. Ferroelec. Freq. Contr., 36:434-441.

Clark, A.E. 1980. "Magnetostrictive Rare Earth-Fe2 Compounds ", Ferromagnetic Materials, 1:532-589.

Clark, A.E. 1992. "High Power Rare Earth Magnetostrictive Materials ", Recent Advances in Adaptive and Sensory Materials and Their Applications , Blacksburg, VA, pp. 387-398.

10.

Crawley, E.F. and K.B. Lazarus. 1991. "Induced Strain Actuation of Isotropic and Anisotropic Plates", AIAA Journal, 29(6):944-951.

11.

Hagood, N.W. and A.A. Bent. 1993. "Development of Piezoelectric Fiber Composites for Structural Actuation", AIAA.

12.

Hashin, Z. and R.W. Rosen. 1964. "The Elastic Moduli of Fiber-Reinforced Materials", J. of Appl. Mech., 31:223-234.

13.

Haun, M.J. and R.E. Newnham. 1986. "An Experimental and Theoretical Study of 1-3 and 1-3-0 Piezoelectric PZT-Polymer Composites for Hydrophone Applications ", Ferroelectrics, 68:123-129.

14.

"IEEE Standard on Magnetostrictive Materials: Piezomagnetic Nomenclature", no. 319.

15.

Ikeda, T. 1990. Fundamentals of Piezoelectricity. Oxford Univ. Press.

16.

Jaffe, H. and D.A. Berlincourt . 1965. "Piezoelectric Transducer Materials", Proceedings of the IEEE, 53(11):1372-1386.

17.

Jensen, H. 1991. "Determination of Macroscopic Electro-Mechanical Characteristics of 1-3 Piezoceramic/Polymer Composites by a Concentric Tube Model", IEEE Tmns. Utrason. Ferroelec. Freq. Contr., 38(6):591-594.

18.

Joshi, S.P. 1992. "Non-Linear Constitutive Relations for Piezoceramic Materials ," Smart Materials and Structures, 1:80-83.

19.

Kannan, K.S. and A. Dasgupta. 1991. "Nonlinear Finite Element Scheme for Modeling the Magneto-Elastic Response of Magnetostrictive Smart Structures ", Smart Structures and Intelligent Syst., Orlando, FL.

20.

Krueger, H. and D. Berlincourt. 1961. "Effects of High Static Stress on the Piezoelectric Properties of Transducer Materials", J. Acoustical Society of America, 33(10):1339-1344.

21.

Moffett, M.B. , A.E. Clark , M. Wn-Fogle , J. Linberg , J.P. Teter and E.A. McLaughlin . 1991. "Characterization of Terfenol-D for Magnetostrictive Transducers", J. Acoust. Soc. Am., 89:1448-1455.

22.

Pagano, N.J. and G.P. Tandon. 1988. "Elastic Response of a MultiDirectional Coated-Fiber Composites", Comp. Sci. and Tech., 31: 273-293.

23.

Parton, V.Z. and B.A. Krudryavtsev . 1988. Electromagnetoelasticity . Gordon and Breach Science Publisher.

24.

Pauley, K.E. and S.B. Dong. 1974. "Analysis of Plane Waves in Laminated Piezoelectric Plates", Wave Electronics, 1:265-285.

25.

Shah, D.K. , S. Joshi and W.S. Chan. 1993. "Comparison of Embedded and Surface Mounted Piezoelectric Actuators," WAM ASME, Adaptive Structures and Materials Systems Symposium, New Orleans .

26.

Wang, D. and G.P. Carman. 1995. "Evaluating the Behavior of Piezoelectric Ceramics Subjected to Thermal Loads", Adaptive Materials Symposium, Summer Conference of AMD/MD ASME, Los Angeles, CA, June.