Surface Electric Displacement Research Articles

Extended mean-field homogenization of unidirectional piezoelectric nanocomposites with generalized Gurtin-Murdoch interfaces

This paper presents for the first time an extended Mori-Tanaka approach aimed at identifying the little-explored piezoelectric response of unidirectional nanoporous composites with energetic surfaces. The interface is simulated using the generalized Gurtin-Murdoch coherent interface model considering nonvanishing in-plane surface stress and surface electric displacement. The analytical solutions for Eshelby’s inhomogeneity problems are obtained by solving four systems of equations, generated from the known macroscopic electromechanical loading conditions. The dilute concentration tensors for the fiber and energetic surface are evaluated exactly for coupled electromechanical fields, which are then utilized in the extended multiphysics Mori-Tanaka homogenization scheme. The reliability and accuracy of the extended theory are demonstrated through an extensive comparison with the predictions of the composite cylinder assemblage (CCA), the generalized self-consistent method (GSCM), as well as the finite-element (FE) homogenization technique. New results generated in this work demonstrate that, except for the transverse shear modulus, the extended Mori-Tanaka, CCA, and FE provide indistinguishable results under axisymmetric, axial shear, and electric loading, even at high volume fractions and small pore sizes where the surface piezoelectric effects are significant.

Homogenization of size-dependent multiphysics behavior of nanostructured piezoelectric composites with energetic surfaces

Surface piezoelectricity considering the extended Gurtin--Murdoch coherent interface model has been incorporated into the composite cylinder assemblage (CCA), generalized self-consistent method (GSCM), as well as the multiphysics finite-element micromechanics (MFEM), for simulating the size-dependent multiphysics response of nanoporous materials wherein interface stress and electric displacement prevail. In the case of the CCA/GSCM model, the coherent interface model is implemented through the generalized Young--Laplace equations that govern the variation of the surface stress and the surface electric displacement. Three loading modes are utilized to identify the closed-form solutions for a complete set of Hill's moduli, and piezoelectric and dielectric constants. In the case of the MFEM, surface piezoelectricity is incorporated directly through additional surface energies associated with the elements that stretch along the interface. In order to assess the accuracy of the developed computational approaches, the generalized Kirsch problem under far-field transverse electric displacement loading is developed for recovering electric displacement concentration in the vicinity of the pore boundary. Homogenized properties are generated and critically examined for a broad variety of parameters and dimensions, predicted by the CCA/GSCM and MFEM methods. It is shown that all the predicted effective properties of these two families of homogenization techniques are similar except for the transverse shear moduli where they show marked differences that are reminiscent of what has been observed in the absence of surface electricity.

Mechanical performance of piezoelectric fiber composites and electroelastic field concentration near the electrode edges

As important smart materials, piezoelectric fiber composites (PFCs) have shown excellent performance in many areas. However, the electric field strength concentration at the edge of the interdigital electrode may lead to crack propagation and eventual actuating failure of PFCs. In this paper, a novel analytical solution on the electroelastic response of PFCs is proposed to characterize the mechanical performance and obtain optimal structure parameters. The problem is converted to a singular integral equation with logarithmic kernel. By solving the resulting equation, the distributions of electric potential, electric displacement, electric field strength, and strain of PFCs fiber are obtained. The finite element method (FEM) is employed to confirm the results. The results demonstrate that the electric displacement and strain of PFCs are dramatically affected by the permittivity properties and piezoelectric constant of materials. The PFCs made by PZT-5H have higher surface electric displacement than PZT-5A and PZT-4. For a ratio of W/L=1/4, both the electric field and strain obtained the minimal value at the electrode edges, which is better for the mechanical performance of PFCs. Moreover, when the thickness of fibers decreases, the actuating performance of PFCs improves and the probability of fracture failure lessens.

The multiple fields created by two perfectly‐conducting punches on piezoelectric/piezomagnetic materials with anisotropy

This article proposes an analytical model of two perfectly conducting punches acting on piezoelectric/piezomagnetic materials with anisotropy. For six types of distinct or repeated roots, related auxiliary function are obtained. The closed‐form solutions of the reduced integral equations are derived for two electrically‐conducting and magnetically‐conducting flat punches. The stress, electric displacement and magnetic induction intensity factors at both edges of each punch are given explicitly in terms of the distance between the two punches and the width of each punch. Numerical test is done to demonstrate the contributions of the distances between the two flat punches and various material properties on the contact behaviors. The obtained results delineate that at the outer edges, there has stronger strength for the singularities of the surface contact stress, surface electric displacement and surface magnetic induction compared with that at the inner edges.

The axisymmetric torsional contact problem of a functionally graded piezoelectric coated half-space

In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.

The interaction of two rigid semi-cylinders over anisotropic piezoelectric materials by the generalized Almansi theorem

An exact contact model of anisotropic piezoelectric materials under the action of two rigid, perfectly conducting semi-cylinders is established. Applying the generalized Almansi theorem arrives at general solutions of related governing equations feasible for both distinctive and repeated eigenvalue cases. Differentiation of the surface vertical displacement and electric potential leads to a system of singular integral equations with a kernel of 1/(ζ2 − x2) type, which is exactly solved by defining proper variables. The surface stresses and the surface electric displacements are given explicitly for two rigid semi-cylinders, which meet the requirements set by the boundary conditions. The results for a single rigid, perfectly conducting cylinder can be covered by those of the two rigid semi-cylinders. The numerical results show how the interaction of two semi-cylinders affects the indentation behaviors and demonstrate that the surface in-plane stress and the surface electric displacement are unbounded at both the inner and outer edges due to the additional electric charge applied on the perfectly conducting semi-cylinder.

Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects

We consider the macroscopic behavior of two-phase fibrous piezoelectric composites. The fibers are of circular cross-section with the same radius. Along the interfaces between the fibers and the matrix we consider the effects of surface stress and surface electric displacement. The constituents are transversely isotropic and exhibit pyroelectricity. We find that the overall thermoelectroelastic moduli of these solids must comply with two sets of exact connections. The first set, similar to Hill’s universal connections, provides five constraints between the six axisymmetric overall electroelastic moduli. The second set relates the effective coefficients of thermal stress and pyroelectric coefficients to the effective electroelastic moduli, in analogy with Levin’s formula. In contrast to their conventional counterparts, i.e., without surface effects, the presence of surface effects makes both sets of connections dependent on the absolute size of the nanoinclusions.