Keywords: piezoelectric composites, smart tubular composites, advanced materials, finite element modelling, numerical simulation.

We present a mathematical modelling and numerical simulation technique for smart tubular composites using a Representative Composite Volume (RCV). Tubular piezocomposites are attractive for applications in biomedicine, flow noise control, aerospace technology, non-destructive testing, automotive instrumentation, various acoustical and oceanographical devices, etc. Here we focus on the so-called 1(0)-3 tubular composites [1] where "1(0)" denotes that one-dimensional ("1") hollow ("0") piezoceramic cylinders are embedded into a three-dimensional ("3") polymer matrix. We consider piezocomposite materials consisting of many piezoelectric hollow cylinders, each with radial polarization, embedded into a passive polymer matrix [2]. The hollow cylinders have electrodes on their inner and outer surfaces, allowing for displacements in both the radial and in the longitudinal directions that depend on the frequency, the inner and outer radii, the length of the tubes and the material properties. The hollow 1(0)-3 piezocomposites are more attractive than the 1-3 type that were previously used in the applications (where piezoceramic rods with longitudinal polarization are embedded in a polymer matrix) mainly because: the radial poling of cylinders is easier to process than the longitudinal poling of rods; the cylinders have lighter weight and higher sensitivity [3].

Here we develop a three-dimensional model of a RCV comprising a symmetrical part of a composite cell. The RCV is free from any mechanical loading, but is subject to a difference of electric potentials on the inner and outer radii of the ceramic cylinder. This is a static boundary-value problem, which we solve by a numerical approximation technique based on the finite element method. We employ the weak variational formulation to the mechanical and electrical equilibrium equations, and after discretization we obtain the corresponding matrix form, which leads to an electro-mechanical coupled linear algebraic system in terms of the mechanical displacements and electric potential.

The solution of the problem exhibits a linear relationship between the maximum mechanical displacement and the applied electrical potential. Moreover, we observe that the maximal mechanical displacement decreases nonlinearly with increasing tube thickness, and increases (nonlinearly) as the height of the cell increases. All the above calculations are with large Young's modulus (about 10GPa) and Poisson's modulus of about 0.3. Further (parametric) results including a variety of polymer (Young's and Poisson's) moduli show that the above behaviour is noted for polymers with large Young's modulus (ranging from 1GPa upwards). However, for polymers with small Young's modulus (no more than 1GPa) the above behaviour is no longer observed. The precise material behaviour is presented by several graphs involving the geometrical and mechanical parameters of the problem.

1

J. F. Fernandez, A. Dogan, Q. M. Zhang, J. F. Tressler, R. E. Newnham, "Hollow piezoelectric composites", Sensors and Actuators, 51(2-3), 183-192, 1995. doi:10.1016/0924-4247(95)01221-4

2

Q.M. Zhang, H. Wang, L.E. Cross, "Piezoelectric tubes and tubular composites for actuator and sensor applications", J. Mater. Sci., 28, 3962-3968, 1993. doi:10.1007/BF00353206

3

R.V.N. Melnik, K.N. Melnik, "Numerical analysis of hollow piezoceramic cylindrical vibrators under non-stationary conditions", Proc. Int. Conf. Eng., Math. and Appl. EMAC'98, 359-362, 1998.

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