Tilted indentation by a flat-ended punch on an anisotropic magnetoelectroelastic half-plane

Abstract

We present closed-form solutions for the indentation of a tilted flat-ended punch with an anisotropic magnetoelectroelastic half-plane. The punch is subjected to a load P at an eccentricity e and the electric charge Ε and magnetic charge I at the same time. The analytical solutions are obtained by utilizing the expanded Stroh formalism for magnetoelectroelastic materials alongside the analytical continuation method. By leveraging Stroh's approach, the general solutions to the problems are expressed in terms of complex variable techniques, which facilitate a comprehensive analysis of the coupled mechanical, electrical, and magnetic fields. The analytical continuation method is utilized to address contact boundary conditions introduced by the tilted punch, enabling the derivation of solutions for stress, electric displacement, and magnetic induction within the half-plane. The punch considered here is flat-ended, and the contact is frictionless. Four electric and magnetic contact conditions are examined. The relations between applied load, electric charge, magnetic charge, angle, and eccentricity of punch are presented in closed-form matrix expressions. As to the case of electric and magnetic insulators, the relation will be further simplified and expressed explicitly in a scalar form. We found that the eccentricity limit and tilted angle limit depend complicatedly on the anisotropic MEE material properties for the cases of (1) electric and magnetic conductor, (2) electric insulator and magnetic conductor, and (3) electric conductor and magnetic insulator. For the case of an electric and magnetic insulator, the eccentricity limit is equal to a/2, where a is the half-width of the punch, which is the same as that of isotropic elastic material. To demonstrate the correctness and versatility of our derived solutions, several numerical examples are provided. Based on the results provided, comprehensive parametric studies on the effects of anisotropic material properties and loadings are also studied and discussed.