Problems of polygonal inclusions in orthotropic materials with due consideration on the stresses at corners

Two-dimensional elastic Green's functions in an orthotropic medium are obtained and expressed in a more explicit and detailed form than those shown in the preceding publications. The stress field associated with a line segment loaded by a uniform traction is found by a direct integration, and it has logarithmic singularities at both ends of the line segment. The basic solutions for the line segment are exploited to solve problems of polygonal inclusions. Stress distributions of circular, triangular, and square inclusions subjected to uniform dilatational eigenstrains in titanium single crystals are presented to show the effectiveness and accuracy of the present approach. The coefficients characterizing the strength of singularity for the stresses at corners are also numerically determined and discussed.