Closed-form solution for a coated circular inclusion under uniaxial tension

A coated circular inclusion embedded in an infinite matrix is analyzed in the framework of two-dimensional isotropic linear elasticity. A closed-form solution is obtained for the case of far-field uniaxial tension using Muskelishvilis complex potential method. The solutions for the stress and strain distributions for all three regions, that is, matrix, coating, and inclusion, were obtained for various coating-to-matrix shear modulus ratios, while keeping the fiber and matrix shear moduli the same. Test cases for an inclusion without the coating and hollow inclusion were also studied. The energy release rate was evaluated using the path-independent M-integral, which is used to calculate the energy release rate for the self-similar expansion of defects surrounded by the closed contour of the integral. The results for the stress and strain concentrations along with the energy release rate due to this material inhomogeneity were analyzed to yield a better understanding of the mechanics of materials with circular inclusions. This can be helpful in designing intelligent composite structures with embedded optical fiber sensors.