On the characterisation of polar fibrous composites when fibres resist bending - Part II: Connection with anisotropic polar linear elasticity

This continuation of Part I (Soldatos, 2018) aims to make a connection between the polar linear elasticity for fibre-reinforce materials due to (Spencer and Soldatos, 2007; Soldatos, 2014, 2015) with the anisotropic version and the principal postulates of its counterpart due to (Mindlin and Tiersten, 1963). The outlined analysis, comparison and discussions are purely theoretical, and aim to collect and classify valuable information regarding the nature of continuous as well as weak discontinuity solutions of relevant well-posed boundary value problems. Emphasis is given on the fact that the compared pair of theoretical models has a common theoretical background (Cosserat and Cosserat, 1909) but different kinds of origin. Some new concepts and features, introduced in Part I in association with linear elastic behaviour of materials having embedded fibres resistant in bending, are thus shown relevant to more general linearly elastic, anisotropic, Cosserat-type material behaviour. The different routes followed for the origination of the compared pair of models is known to produce identical results in the case of conventional (non-polar) linear elasticity. The same is here found generally not true in the polar elasticity case, although considerable similarities are also observed. No definite answers are provided regarding the manner in which existing differences might be bridged or, if at all possible, eliminated. These are matters that require further study and thorough investigation.