Abstract
The Asymptotic Homogenization Method (AHM) is applied to a family of boundary value problems for linear thermo-magneto-electro-elastic (TMEE) heterogeneous material with rapidly oscillating coefficients and magneto-electro-elastic imperfect contact between the phases. Using matrix notation we show the procedure for constructing a formal asymptotic solution that leads to the homogenized problem, the effective coefficients and the local problems. The effective coefficients are functions of the solutions of the local problems, which, in the case of a laminate, reduce to systems of ordinary differential equations. The methodology is illustrated with an example of a two-phase piezoelectric/piezomagnetic laminate formed by transversally isotropic phases. The analytical expressions of the effective moduli work for any number of phases and show a marked dependence on the values of the magneto-electro-elastic imperfect contact parameters. It is also shown that some moduli satisfy exact relations that allow us to compute them when the values of some other modulus is given. The numerical examples show the emergence of product properties such as the magneto-electric, pyromagnetic and pyroelectric effects.
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