Fundamental solutions to contact problems of a magneto-electro-elastic half-space indented by a semi-infinite punch

• A half space of multi-ferroic composite is indented by a half-infinite punch.
• Electro-magnetic properties of the indenter are taken into consideration.
• Potential theory is extended to the contact problem in magneto-electro-elasticity.
• Fundamental field variables are expressed in terms of elementary functions.
• Stress singularity in the generalized stress is discussed.

This paper presents the fundamental contact solutions of a magneto-electro-elastic half-space indented by a smooth and rigid half-infinite punch. The material is assumed to be transversely isotropic with the symmetric axis perpendicular to the surface of the half-space. Based on the general solutions, the generalized method of potential theory is adopted to solve the boundary value problems. The involved potentials are properly assumed and the corresponding boundary integral equations are solved by using the results in literature. Complete and exact fundamental solutions are derived case by case, in terms of elementary functions for the first time. The obtained solutions are of significance to boundary element analysis, and an important role in determining the physical properties of materials by indentation technique can be expected to play.