The elastic field distributions in damaged composite half-planes created by various surface loadings

A method of solution is presented for the prediction of the elastic field distributions in composite half-planes possessing periodic microstructure and embedded internal damage. The elastic field is created by the application of a compressive loading on a portion of the half-plane surface or by its indentation by rectangular, circular or wedge-shaped rigid punches. The method is based on a two scale (micro-to-macro) analysis. In the microscale analysis, a micromechanical model is employed for the determination of the effective stiffness tensor of the undamaged composite. This is followed by a macroscale analysis where the partially loaded composite half-plane which consists of distinct phases and an embedded damage is considered. The macroscale analysis consists of the solution of an auxiliary elasticity problem, followed by the application of the discrete Fourier transform in the domain of which the damaged composite problem is solved in conjunction with an iterative procedure and the transform inversion. Applications and verifications are given for a half-plane which consists of a porous alumina that includes a damage in the form of a short crack, a semi-infinite (long) crack or a rectangular hole.