Elliptical inhomogeneity in orthotropic composite materials due to uniform eigenstrains

Abstract

Analytic solutions are presented for elastic fields induced by normal and shear eigenstrains in an elliptical region (inhomogeneity) embedded in orthotropic composite materials (matrix). Conformal transformation and complex function method are adopted to obtain exact stress distributions in the matrix at the interior boundary to calculate strain energy in the matrix. The stress fields in the elliptical inhomogeneity are derived analytically based on application of the principle of minimum strain energy of the elastic system to determine two fundamental variables characterizing the equilibrium boundary. The resulting solutions are verified with the continuity conditions for the normal and shear stresses along the interior boundary of the matrix. These reduce to known results for some special cases. Numerical examples are provided to illustrate the resulting solutions to the analysis of stress distribution pattern, strength-based failure and fracture behavior. The proposed model can be applied to evaluate volumetric expansion induced cracking and failure of polymers and polymer composites due to freezing of trapped moisture in the elliptical inhomogeneity region as well as fatigue strength of the materials under freeze–thaw conditions.