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, $−∞. In the present paper, it is found that the analytical solutions within the region $x12+x22>a2,−∞ 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.

1.
Chiu
Y. P.
,
1977
, “
On the Stress Field Due to Initial Strains in a Cuboid Surrounded by an Infinite Elastic Space
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
44
, pp.
587
590
.
2.
Eshelby
J. D.
,
1957
, “
The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems
,”
Proceedings of the Royal Society, London
, Vol.
A241
, pp.
376
396
.
3.
Eshelby
J. D.
,
1959
, “
The Elastic Field Outside an Elastic Inclusion
,”
Proceedings of the Royal Society, London
, Vol.
A252
, pp.
561
569
.
4.
Hasegawa
H.
,
Lee
V. G.
, and
Mura
T.
,
1992
, “
The Stress Fields Caused by a Circular Cylindrical Inclusion
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
59
, pp.
S107–S114
S107–S114
.
5.
Karihaloo
B. L.
, and
Viswanathan
K.
,
1988
, “
A Partially Debonded Ellipsoidal Inclusion in an Elastic Medium. Part 1: Stress and Displacement fields
,”
Mechanics of Materials
, Vol.
7
, pp.
191
197
.
6.
Lee
Mikyoung
,
Jasiuk
I.
, and
Tsuchida
E.
,
1992
, “
The Sliding Circular Inclusion in an Elastic Half-Plane
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
59
, pp.
S57–S64
S57–S64
.
7.
Mura, T., 1987, Micromechanics of Defects in Solids, Martinus Nijhoff.
8.
Mura
T.
,
1988
, “
Inclusion Problem
,”
ASME Applied Mechanics Review
, Vol.
41
, pp.
15
20
.
9.
Sankaran
R.
, and
Laird
C.
,
1976
, “
Deformation Field of a Misfitting Inclusion
,”
Journal of the Mechanics and Physics Solids
, Vol.
24
, pp.
251
262
.
10.
Seo
K.
, and
Mura
T.
,
1979
, “
The Elastic Field in a Half Space Due to Ellipsoidal Inclusions With Uniform Dilatational Eigenstrains
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
46
, pp.
568
572
.
11.
Takao
Y.
,
Taya
M.
, and
Chou
T. W.
,
1981
, “
Stress Field Due to a Cylindrical Inclusion with Constant Axial Eigenstrain in an Infinite Elastic Body
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
48
, pp.
853
858
.
This content is only available via PDF.