The response of a partially loaded composite half-space weakened by local defects

The elastic field in a fiber-reinforced half-space which consists of distinct constituents and localized internal defects is predicted by employing a multiscale analysis. A normal distributed uniform loading is applied over a rectangular region of the half-space surface, while the other parts are kept traction-free. The effect of internal defects and the half-space traction-free boundary conditions are accounted to by incorporating a damage tensor in the constitutive relations which describe the half-space phases. In the micro level of the micro-to-macro analysis, the effective behavior of the composite half-space is determined by employing a micromechanics analysis. This is followed by a macromechanical analysis in which the triple discrete Fourier transform is applied in the domain of which the formulated problem is solved. The damaged composite half-space response is obtained by inverting the Fourier transform, in conjunction with an iterative procedure. The predicted elastic field in the half-space which is based on the present approach is validated by comparisons with exact and finite element solutions. The offered method is applied to generate the elastic field in a fiber-reinforced half-space with a broken fiber, lost fiber, debonded fiber, missing fiber and a matrix void. Applications of numerous defects of these and other types are discussed.