Higher order interface conditions for piezoelectric spherical hollow composites: asymptotic approach and transfer matrix homogenization method

The paper describes the mechanical behavior of composites made of piezoelectric spheres in perfect or imperfect contact. The imperfect contact is achieved by interposing piezoelectric thin adhesive layers between the spheres. First, using asymptotic analysis, transmission conditions of imperfect interface equivalent to the behavior of piezoelectric adhesive layers are obtained at order 0 and 1. These transmission conditions are calculated for hard adhesives, i.e. adhesive materials whose electromechanical constants do not rescale with their thickness. Next, under the assumption of spherical symmetry, the transmission conditions are condensed to a general law of imperfect contact, able to simultaneously describe different contact regimes: piezoelectric hard (order 0 and 1) and soft (or spring-type, order 0 and 1) interface conditions, the perfect continuity conditions, and the piezoelectric rigid (Gurtin-Murdoch or membrane-type) conditions. Lastly, following Bufler's approach, the homogenization problem of a spherical hollow piezoelectric assembly is solved, extending the classical transfer matrix method to take into account the presence of thin adhesive layers described using the proposed transmission conditions of imperfect contact. A simple numerical example is provided, illustrating the correctness and effectiveness of the homogenization approach in describing the electromechanical behavior of spherical piezoelectric assemblies.

Automated summary

This paper discusses the mechanical behavior of composites made of piezoelectric spheres and introduces imperfect contact and thin piezoelectric adhesive layers. By asymptotic analysis and spherical symmetry assumption, transmission conditions for different contact regimes, general laws of imperfect contact, and a homogenization solution for spherical hollow piezoelectric assemblies are obtained. A numerical example demonstrates the effectiveness of the approach in describing the electromechanical behavior of spherical piezoelectric assemblies.