Modelling the piezoelectric effect in a composite polymer film filled with disperse piezoelectric

Mesoscopic modelling of a composite material constituted by an electroneutral polymer (matrix) film filled with micropowder of piezoelectric ceramics (filler) is presented. The calculation scheme resembles that of the RVE (Representative Volume Element) method. The representative element (cell) is a right-angle prism with square cross-section, the height of which is equal to the film thickness. Around the midsection of the prism, there are a few (from 2 to 4) spherical piezoelectric particles positioned close to one another. The length of the base side of the prism is determined from the assumed solid phase content of the composite. To simulate the film, the cells are arranged in a continuous flat layer, inside which they are coupled by means of periodic boundary conditions imposed on their lateral surfaces. To reduce the artifacts of the model, the position of the center of each particle is chosen randomly within the area of the prism cross-section. In the framework of this approach, a low-density polyethylene film with embedded barium titanate particles is considered as an example. One of the surfaces of the film is fixed (no displacements), and the other one is left free. For the characteristics of the particles close to those used in the experiment and the typical matrix material parameters (elasticity moduli, Poisson coefficients, dielectric permittivity), the voltage output (piezoeffect) induced in the film in response to the uniform pressure applied to its free surface is evaluated. It is shown that the electric potential along the thickness of the film is nonuniform: it grows inside the particles and falls down in the interparticle gap. In order to present the results in the form applicative for comparison with the experimental data, for each variant of the system (number of the particles, weight fraction of the solid phase), the calculated values are averaged over a few tens of realizations of the particle positions inside the element.