Temperature-related effective properties and exact relations for thermo-magneto-electro-elastic fibrous composites

Two-phase periodic thermo-magneto-electro-elastic composites are considered. The composite materials consisting of identical parallel cylindrical fibers periodically distributed in a matrix. Both constituents are transversely isotropic and the unit-cell has rhomboidal shape. Based on the asymptotic homogenization method, exact relations involving the in-plane effective coefficients are derived without imposing any restriction on the global behavior of such fibrous composite materials. The proof is based on the existence of invariant conditions at the interface linking the solutions of six local problems. In particular, proportionality relations linking the temperature-related effective coefficients are obtained. Simple analytical formulae are obtained for these temperaturerelated effective coefficients as a function of four effective elastic coefficients, and they show the existence of pyroelectric and pyromagnetic product properties in the composite material when these effects are not present at the constituents level. These results for the in-plane effective coefficients were reported in [1]. Here, also exact relations for the antiplane effective coefficients are obtained by applying the theories of [2, 3]. A regularity for the corresponding compatibility conditions is found. Comparisons with analytical and numerical results are included. [1] Bravo-Castillero, J., Sixto-Camacho, L.M., Brenner, R., Guinovart-Díaz, R., L.D. Pérez-Fernández, Rodríguez-Ramos R., Sabina, F.J., 2015. Temperature-related effective properties and universal relations for thermo-magneto-electro-elastic fibrous composites, Computers and Mathematics with Applications 69 (9), 980-996. [2] Milgrom, M., Shtrikman, S., 1989. Linear response of two-phase composites with cross moduli: Exact relations universal, Phys. Rev. A 40 (3), 1568-1575. [3] Milgrom, M., 1997. Some more exact results concerning multifield moduli of two-phase composites, J. Mech. Phys. Solids 45 (3), 1399-1404.