The present paper deals with a general asymptotic theory aimed at deriving some imperfect interface models starting from thin interphases. The novelty of this work consists in taking into account some non-standard constitutive behaviors for the interphase material. In particular, micro-cracks, surface roughness and geometrical nonlinearity are included into the general framework of the matched-asymptotic-expansion theory. The elastic equilibrium problem of a three-composite body comprising two elastic adherents and an adhesive interphase is investigated. Higher order interface models are derived within the cases of soft and hard interphase materials. Simple FEM-based numerical applications are also presented.
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