Field distributions in cracked periodically layered electromagnetothermoelastic composites

Abstract

A novel approach is employed for the prediction of stress, electrical, and magnetic fields generated by applying combined loadings on damaged composites that consist of periodic electromagnetothermoelastic layers. The damage may represent cavities and cracks and must be localized in the sense that its effect on the remote-loaded boundaries of the composite is negligible. This approach is based on the combined use of the representative cell method, the higher-order theory, and the high-fidelity generalized method of cells micromechanical model. In the framework of the representative cell method, the problem for a periodic composite that is discretized into numerous identical cells is reduced to a problem of a single cell in the discrete Fourier transform domain. In the framework of the higher-order theory, the resulting governing equations and interfacial conditions in the transform domain are solved by dividing the single cell into subcells and imposing the latter in an average (integral) sense. The high-fidelity generalized method of cells is utilized for the prediction of the proper far-field boundary conditions, which are based on the unperturbed effective properties of the composite. The inverse of the Fourier transform provides the real elastic field at any point of composite with localized effects. The damage existence is modeled by introducing fictitious unknown eigenfields that are computed by an iterative procedure. This modeling is verified by a comparison with five analytical solutions of cavities and cracks embedded in piezoelectric and electromagnetoelastic materials. Several applications of cracked layered composites are given.