On thermal coefficients of thermo-magneto-electro-elastic N-laminates

Abstract

In linear context, it is known that for n-phase 1D laminated structures, the effective magneto-electro-elastic (MEE) stiffness and compliance moduli tensors are exactly obtained from solving the generalized stress-strain relations from the “consistency phase boundary conditions” (CBC) of uniform gstresses and uniform gstrains normally and transversally to the layers respectively. This exact solution for laminates, although not referring to any homogenization framework, identifies with all (Hashin-Shtrikman, Mori-Tanaka, Self-Consistent, …) estimates which coincide at this order. Recently, the author has shown that it furthermore obeys a “generic” explicit simple form resulting from an essential property of the strain and stress dual Green operators (GOs) for infinite layers directionally stacked to form an infinite medium. This solution form is here examined in the extended affine context when thermal (T) gstresses and gstrains are accounted for as eigen-fields additional to the MEE ones. Explicating effective TMEE-coupled properties from this route corresponds with a specific form of the TMEE generalized Levin's (1967) formula for laminates, based on solely knowing the dual strain and stress laminate GOs. The obtained stress and strain thermal eigen-vector terms from this affine approach are examined in terms of their elastic, electric and magnetic components for the well documented case of two-phase BaTiO3–CoFe2O4 TI laminates.