Compliance functions of electromagnetoelastic piezoelectric and piezomagnetic half-plane and half-space with functionally graded or layered coatings

The paper addresses to the construction of the compliance functions of axissymmetric and plane contact problems of electromagnetoelasticity for semi-infinite piezoelectric piezomagnetic solids with functionally graded or piece-wise homogeneous coatings. Materials of coating and substrate are assumed to be transversely isotropic. Computation of the compliance functions are reduced to the solution of two-point boundary value problems for a system of ordinary differential equations with variable coefficients are obtained using integral transformation technique. Boundary conditions of these systems describe distributed tangential or normal mechanical loading or action of an electrical of magnetic fields.
Dual integral equations and their systems are obtained for contact problems on indentation by an insulating and conductive punches with kernel transforms equal to compliance functions. Asymptotic behavior of the compliance functions is analyzed.
Specially designed approximations for the kernel transforms are constructed based on the analysis of their properties. These approximations make it possible to construct the solutions of the approximated systems of dual integral equations in a closed analytical form. Numerical results illustrating all 10 independent compliance functions are provided for different materials of coating and substrate and different types of variation of properties in depth of the coating.
It is shown that in the case of absence of the tangential mechanical loading all the compliance functions are positive. Conditions of existing sign alternating compliance functions corresponding tangential mechanical loading are analyzed. The differences between the properties of the compliance functions, corresponding to homogeneous and functionally graded coatings are illustrated.