Structure of the generalized echelby problem solution and gauss representation for homogeneous polynomials

Volkov-Bogorodsky D.B.

Abstract:

Solutions of the generalized Eshelby problem with polynomial displacements at infinity are investigated in elasticity theory for spherical and cylindrical multilayer inclusions. Such problems arise in the asymptotic averaging method for the viscoelasticity equations with rapidly oscillating coefficients. They are used for accurately calculating effective characteristics of the composite materials. To solve this problem we use the Gauss representation for homogeneous polynomials and it’s related potentials of Papkovich-Neuber representation that resolve the Eschelby problem in finite algebraic form.