The Elastic Field Caused by a Circular Cylindrical Inclusion—Part II: Inside the Region x12 + x22 > a2, −∞ < x3 < ∞ Where the Circular Cylindrical Inclusion is Expressed by x12 + x22 ≤ a2, −h ≤ x3 ≤ h

Abstract

Analytical solutions are presented for the displacement and stress fields caused by a circular cylindrical inclusion with arbitrary uniform eigenstrains in an infinite elastic medium. The expressions obtained and those presented in Part I constitute the solutions of the whole elastic field, −∞ < x1, x2, x3 < ∞. In the present paper, it is found that the analytical solutions within the region x12 + x22 > a2, −∞ < x3 < ∞ can also be expressed as functions of the complete elliptic integrals of the first, second, and third kind. When the length of inclusion tends towards the limit (infinity), the present solutions agree with Eshelby’s results. Finally, numerical results are shown for the stress field.