Determination of the spherical part of the couple-stress in a polar fibre-reinforced elastic plate subjected to pure bending

Abstract

Abstract This communication provides initial information and understanding of the manner in which a newly developed theoretical mechanism (Soldatos in Int J Solids Struct 202:217–225, 2020) is applied in specific boundary value problems met in polar linear elasticity of fibrous composites and thus enables the determination of the spherical part of the couple-stress tensor. In this context, it tests the applicability of the implied mechanism/method in the case that a rectangular plate reinforced by a single family of unidirectional fibres is subjected to pure bending. The problem solution is obtained for either non-polar or polar material behaviour, where fibres are considered perfectly flexible or resistant in bending, respectively, and provides clear evidence of the correctness of the principal argument that underpins the proposed method. Namely, that the general rotation field of the plate deformation differs from the fibre rotation field. That newly discovered method enables an extra energy term that emerges in the strain energy function of the fibrous composite plate to relate with the spherical part of the couple-stress tensor outside conventional equilibrium conventions. It thus leads to the determination of the spherical part of the couple-stress and its distribution throughout the plate body in a complete and comprehensive manner.