Phase mean strain and stress estimates in possibly multi-continuous composites under affine elastic-like behavior

N-phase materials (perfect phase bonding, no cracks) can have one single, several or none continuously through-sample spanning (i.e. topologically continuous or connected) phases. The former phase assemblage type is known as the inclusion-matrix structures (all but one phase are discontinuous hence embedded) and the latter one is a special case of aggregates. The type when several p phases -possibly up to all -among n are arranged such as to be simultaneously (co-) continuous, to be called multi-continuous composites, gathers all the other assemblage possibilities, of greatest number for n > 3. Earlier works from the author and co-workers proposed specific linear elastic-like (i.e. including piezo-type coupling) effective property estimates for any n > p > 2, from making use of laminate system (LS) schemes, within the Hashin-Shtrikman (HS) mean field homogenization framework. The characteristics of these LS estimates likely to represent p-phase co-continuity were identified in comparing with the related ones for inclusion-matrix structures and for random aggregates. The objective is here to examine the phase (mean) strain and stress estimates that result from the localization counterparts of the LS schemes, in broadening the framework to affine elastic-like behavior, i.e. linear elastic-like with phase eigen-strains. One makes use of the previous result firstly recalled that each phase assemblage type, regardless of complexity va-rieties, can be mainly characterized by a specific (n + 1)th reference medium layer with null concentration. The localization characteristics are then examined from this theoretical viewpoint for n-phase composites, special-izing for the two-phase LS(A,B) estimates which we compare with the HS(A,B) ones for the A in B and B in A phase arrangements. Specific LS(2) localization features are pointed.

Automated summary

This passage discusses the different ways in which phases in multi-phase materials can be connected, and the effective property estimates obtained through specific methods, especially in the analysis of multi-continuous composites. The author proposes that the estimates obtained using laminate system schemes within the mean field homogenization framework may represent specific phase co-continuity characteristics.