On a two-component elastic mixture with different temperature values in a scalar field

In this paper, we study the static case of the two-temperature theory of elastic mixtures, when partial displacements of the elastic components of the mixture have equal values. The contact problem with a ball bounded by the contact spherical surface is considered. The ball is filled with a composite material, while the external scalar field of the ball is defined by a harmonic function. The representation formula obtained for a general solution of a system of static homogeneous differential equations of the two-temperature theory of elastic mixtures is expressed by means of four harmonic and one metaharmonic functions. The theorem stating the uniqueness of a contact problem solution is proved. The problem solution is obtained in the form of absolutely and uniformly convergent series.