Three-Dimensional Green's Functions For Electro-magneto-thermo-elastic Materials

Green's functions or fundamental solutions play an important role in both applied and theoretical studies on the physics of solids. They are a basic building block of a lot of further works including numerical calculation and theoretical analysis. Electro-magneto-thermo-elastic material is a new type of composite material which contains simultaneously piezoelectric, piezomagnetic, magnetoelectric, pyroelastic, pyroelectric and pyromagnetic effects. Because it particularly contains thermo- magneto-electro-elastic performance, it is used widely in smart structures and intelligent structure systems.Concerning the Green's functions or fundamental solutions studies of electro- magneto-thermo-elastic material, many references only research electro–magneto- mechanical coupling behavior in isothermal case. This is mainly because adding thermal coupling equations breaks the fine properties of the pristine equations, which increases the troubles. However, for the smart structures and intelligent structure systems constructed with electro-magneto-thermo-elastic materials, their practical work environment is universally not isothermal. This makes the thermal coupling effects of electro-magneto-thermo-elastic materials not avoid.Against this background, as the study object of the familiar transversely isotropic electro-magneto-thermo-elastic engineering material, the three-dimensional Green's functions are presented respectively for a semi-infinite, an infinite and two-phase transversely isotropic electro-magneto-thermo-elastic material with a steady point heat source, point force, point charge and point magnetic monopole acting.Firstly, the non-dimensional steady general solution of transversely isotropic electro-magneto-thermo-elastic material is described. For various kinds of point load in infinite transversely isotropic electro-magneto-thermo-elastic material, their fundamental solutions can be obtained by constructing five new harmonic functions. The constants of the harmonic functions are determined by using the compact general solution of transversely isotropic electro-magneto-thermo-elastic material, and considering the corresponding equilibrium and continuity conditions.Three-dimensional Green's functions for various kinds of point load on the surface and in the interior of a semi-infinite transversely isotropic electro–magneto- thermo-elastic material can be obtained by introducing five new suitable harmonic functions respectively. The corresponding constants are determined by using the compact general solution of transversely isotropic electro–magneto-thermo-elastic material, and considering the corresponding boundary, equilibrium and continuity conditions.According to the same method, the three-dimensional Green's functions for various kinds of point load in two-phase electro-magneto-thermo-elastic materials is presented by introducing ten new harmonic functions. The corresponding constants are determined by using the compact general solution of transversely isotropic electro- magneto-thermo-elastic material, and considering the corresponding boundary and equilibrium conditions.Finally, numerical results of corresponding coupled fields are given graphically by contours, including temperature increment, stress, electric displacement and magnetic induction. Meanwhile the contours are analyzed, and some valuable engineering conclusions are obtained by analyzing contours.