Multiple continuity of phases in composite materials: Overall property estimates from a laminate system scheme

With the subsequent goal of estimating effective properties of general n-phase composites, a recent (2016) paper from the author and a co-worker firstly addressed all elementary situations of one-level phase arrangements from all to none phases being co-continuous and proposed relevant property estimates within the mean field approximation homogenization framework. At the first time to the authors knowledge was proposed an estimate for the arrangements (that occur from 3 phases and are the main type above 3) when several but not all the assembled phases are co-continuous. Use was made of a laminate system (LS) scheme method inspired from a literature of the sixties on fiber system schemes likely to ensure phase co-continuity. Laminate systems were similarly figured as interpenetrated one-directional layered structures with layer normal oriented in various directions of space, a realizable representation of which can be multiple slip activity in crystals. The relevancy of using such a IS scheme to obtain stiffness property estimates that account for phase co-continuity in composites was then successfully exemplified for various, elastic-like or other (piece-wise) linear properties and the possible use of a dual scheme in terms of compliances was shown to likely correspond to a sort of phase co-discontinuous converse assemblage. After a few recalls and a clarification of this co-continuity/co-discontinuity duality, we propose a description of a general phase arrangement from a specified combination of the elementary ones. Testing it on a two-phase disordered assemblage, a remarkable relation between elementary estimate types is established that comes in support to the relevancy of the proposed description and to the one of the dual IS schemes to accounting for multiple phase continuity. A short application on experimental literature data is also exemplified. (C) 2019 Elsevier Ltd. All rights reserved.