A numerical estimation of the effects of a cylindrical hole and imperfect bonding on stability of a fibre in an elastic matrix

A simple numerical model based on three-dimensional analytical considerations is proposed for an estimation of the local e ects of a cylindrical hole in the matrix as well as of bre{matrix interface imperfections on compressive stability of bres in bre-reinforced composites. The geometry of the model includes an inclusion (a bre) in a matrix with the assumption of an imperfect bonding at the interface and a cylindrical hole in the closest neighbourhood. Then the problem formulation is idealized in two directions, providing a possibility of establishing lower and upper bounds for critical loads for the case of a matrix with a cylindrical hole of a non-circular cross-section as well as for the case of interface imperfections with the possibility of sliding without discontinuity of the displacements normal to the interface. The model takes into account the distinct di erence in the properties of the bre and the matrix and the spatial character of the problem at the microlevel. It is based on individual consideration of the bre and the matrix with a hole with the necessity of satisfying certain idealized bonding conditions between them