Transversally isotropic Magneto-Electro-Elastic composites with co-(dis) continuous phases

The author and his co-workers have recently shown that for materials with several to all co-continuous phases, effective elastic moduli were well approached from microstructure descriptions combining “laminate and fibre systems” as introduced in the seventies and that, provided either a moduli or a compliance approach, laminate systems were likely to describe materials with either all co-continuous or all co-discontinuous phases (sample spanning clusters of all or of none phases resp.). Aside of aggregate assemblages or of inclusion/matrix structures, they represent two other important classes of material architectures. The effective properties of such “co-(dis) continuous composites” for short, as described by laminate systems, are here examined in the enlarged context of coupled Magneto-Electro-Elastic (MEE) properties in overall transversal isotropy (TI). One illustrates and comments in the two-phase case significant comparisons of property estimates from laminates systems (LS) with the extensions to the MEE context of the classical Hashin–Shtrikman (H–S) and Self-Consistent (S-C) estimate types in the simplest but representative situation of axially fibered composites along the TI symmetry axis. The here pointed importance of the introduced two LS estimates is that, while for two phases, the H–S estimate types correspond with two of the only four possible phase arrangements, the LS estimate types correspond with the two other ones. As a consequence, provided the occurrence probability of each of the four arrangements, using all four (H–S and LS) estimate types as extended for a given coupling context must allow to approaching the effective properties of any two-phase mixture in this coupling context. In support to this claim, a simple example is given, anticipating a forthcoming paper to be fully dedicated to this opened new way for modeling and tuning, from two to more phases, the effective properties of complex architectures.