The behavior of cracked multiferroic composites: Fully coupled thermo-electro-magneto-elastic analysis

The response of cracked multiferroic composites that are subjected to thermo-electro-magneto-elastic loading is established by employing a two-scale analysis. To that end, the fully coupled constitutive and governing equations are utilized in the analysis. This form a generalization of a one-way thermal coupling analysis in which the electro-magneto-elastic field does not affect the thermal field. The micro-scale analysis is based on a micromechanical model which is capable of predicting the effective stiffness tensor of the undamaged multiferroic composite as well as the concentration tensors which enable the computation of the local field from the applied thermo-electro-magneto-elastic far-field. The macro-scale analysis provides the response of the cracked composite of periodic microstructure to the applied loading. It is based on the combined use of the representative cell method and the higher order theory. In the framework of the representative cell method, the problem for a periodic composite which 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 governing equations and interfacial and periodic conditions formulated in the transform domain are solved by dividing the single cell into several subcells and imposing these conditions in an average (integral) sense. Results exhibit the responses caused by the application of mechanical, electric, magnetic, thermal, and heat flow loadings on two types of cracked periodically layered composites and provide comparisons between the predictions of the full and one-way thermal coupling analyses.