Asymptotic homogenization of periodic thermo-magneto-electro-elastic heterogeneous media

The asymptotic homogenization method is applied to a family of boundary value problems for linear thermo-magneto-electro-elastic (TMEE) heterogeneous media with periodic and rapidly oscillating coefficients. Using a matrix notation, the procedure for constructing the formal asymptotic solution is described. Two ways to validate the asymptotic analysis are explained. The main differences/similarities with respect to the asymptotic homogenization models reported in recent papers are remarked. The analytical expressions for effective coefficients of laminated media with any finite number of anisotropic TMEE layers are explicitly obtained via the matrix notation. Such formulae can be applied to investigate the global behavior of functionally graded TMEE multilayers. The important case of bilaminates composites with anisotropic homogeneous phases is also expressed in a compact form using matrices and vectors depending on the individual geometrical and mechanical properties of the components. The case of a bilaminate with homogeneous transversely isotropic TMEE layers is studied. A chain of equalities relating all thermal (thermoelastic, pyroelectric, pyromagnetic and heat capacity) effective coefficients was found for the example corresponding to a parallel connectivity. An analytical formula to estimate the volume fraction for which the pyroelectric and pyromagnetic effects realize their extreme values is given. Comparisons with recently published results are included.