Representation formulae of general solutions in the theory of hemitropic elasticity

We consider the steady state oscillation equations of the theory of elasticity of hemitropic materials. We derive general representation formulae for the displacement and microrotation vectors by means of six scalar metaharmonic functions. These formulae are very convenient and useful in many particular problems for domains with concrete geometry. Here we consider two canonical transmission problems for piecewise homogeneous bodies with spherical interfaces and with the help of the representation formulae construct explicit solutions in the form of absolutely and uniformly convergent series. The representations can also be applied to multi-layered bodies with spherical and cylindrical interfaces.