Dynamic field distributions generated by localized effects in periodically layered composites

The time-dependent elastic field generated by the sudden formation of localized cracks in periodically layered composites which has been initially subjected to a system of stresses is determined. Similarly, the elastic field caused by the diffraction of an incident plane pulse in elastic material with a localized crack, cavity or inclusion is established. As a result of these localized effects the periodicity of the system is lost and a repeating unit cell in the composite cannot be identified and analyzed anymore. These effects are represented, in conjunction with the continuum damage mechanic concepts, by eigenstresses which for the general case of an orthotropic constituent include nine independent damage variables. The method of solution is based on the combination of two distinct approach. In the first one, the representative cell method is employed according to which the periodic composite, which is discretized into several cells, is reduced to a problem of a single cell in the discrete Fourier transform domain. The resulting elastodynamic equations, initial, boundary and interfacial conditions in the transform domain are solved by employing a wave propagation in composite analysis which forms the second approach. This theory has been presently generalized to include the initial stresses in the composite and to accommodate the eigenstresses which include the damage variables. The accuracy and reliability of the present method of solution is verified by comparisons with five different cases where either analytical solutions are available or a different method of analysis is used. Five applications are presented which include, in particular, the prediction of the dynamic field generated by the sudden appearance of H-cracks in a periodically layered ceramic matrix composite that is subjected to initial in-plane tension, in-plane and out-of-plane shears.