Remarkable correspondence between multilayer stacks and multi-coating platelets: From generalized composite inclusion to polarization tensor of platelets

Abstract

The intimate connection between configurations as well as numerical results of multilayer stacks and thin, multiply coated platelets prompted the present study to probe deeper into their relationships. The paper presents the derivation of the effective stiffness of multilayer stacks by generalizing the composite inclusion model (GCIM) to the most general layout, with any form of anisotropy for constituent layers. Despite the extensive mathematical derivation procedure and rather long equations obtained at the end, it is mathematically demonstrated that GCIM is identical with the much simpler two-phase CIM that is recursively used in a layer-wise sweep and replacement framework. Then a geometrical and mathematical correspondence is established between thin, multiply coated platelets and a class of symmetric multilayer stacks. The outcome of the remarkable correspondence between GCIM (for multilayer stacks) and an Eshelby-type estimator (for coated platelets) is the most compact, closed-form polarization tensor of thin, ellipsoidal platelets. Subsequent validation of this significant result corroborates the presented methodology. Finally, the simplest and shortest identification algorithm for characterizing an unknown constituent in any multilayer stack and any multi-coating platelet is formulated based on the findings of the investigation. By following a similar procedure, the results and conclusions of the study can be similarly extended to other physical properties.