Surface-energetic piezoelectric materials and effective properties of composites in antiplane loading conditions

A surface piezoelectricity model generalizing the Steigmann–Ogden model for linear elastic solids is described starting from a rigorous variational approach. The boundary and tip conditions on surface-energetic material surfaces are presented. The model is applied to the problem for a one-phase or a two-phase piezoelectric circular fiber in a piezoelectric infinite matrix. The piezoelectric materials are assumed to have a 6-mm hexagonal crystal symmetry. The problem is solved analytically using the complex variable approach. The boundaries between different materials possess surface piezoelectric energy. The matrix is subjected to a far-field loading and contains a piezoelectric screw dislocation. The effective moduli of the piezoelectric composites reinforced by one-phase or two-phase circular fibers are obtained using the Maxwell’s far-field methodology. The results are compared with the generalized self-consistent scheme. An image force on the dislocation is computed using the generalized Peach–Koehler formula. Numerical examples and parametric studies are presented.