Micromechanical investigation of thermal stresses of a finite plane containing multiple elliptical inclusions based on the equivalent inclusion method and distributed dislocation method

This paper presents a micromechanical method to analyze the thermal stresses in a finite plane containing multiple elliptical inclusions. Firstly, the Eshelby’s equivalent inclusion method is employed to solve the elastic fields of a two-dimensional infinite plane containing multiple elliptical inclusions under a uniform temperature change. Both the interior Eshelby’s tensor and the exterior Eshelby’s tensor are employed. Then the boundary of the plane is modeled by continuous distributions of dislocation densities. By combining the two steps, a system of singular integral equations is formulated based on the traction-free boundary condition. Then the thermal stresses of the plane can be obtained by the superposition of the stresses obtained by the Eshelby’s equivalent inclusion method and distributed dislocation method. Additionally, some examples are given to show the effects of the presented method. The effects of the material constants, geometric parameters and fiber packing arrangement on the thermal stresses are also studied.