On the constitution of polar fiber-reinforced materials

Soldatos, K. P.; Shariff, M. H. B. M.; Merodio, J.

Abstract

This article presents important constitutive refinements and simplifications in the theory of polar elasticity of materials reinforced by a single family of fibres resistant in bending. One of these simplifications is achieved by paying attention to forms of the strain energy which are symmetric with respect to the symmetric and the antisymmetric parts of the fibre gradient tensor. This leads to the identification of a restricted version of the theory that is predominantly influenced by the fibre-splay mode of deformation. The lack of ellipticity of the governing equations of polar elasticity and the anticipation of existence of weak discontinuity surfaces even in the small deformation regime are also investigated. The manner in which potential activation of such surfaces is related with the action of either the fibre-bending or the fibre-splay deformation mode, as well as with their conjoined combination and coupling with their fibre-twist counterpart, is examined. The proposed constitutive equations can be simplified via the use of a new set of fourteen independent spectral invariants of the deformation. This set serves as an irreducible functional basis of relevant invariants or as an irreducible integrity basis of polynomial invariants. For instance, its use here enables identification of fourteen classical invariants that emerge as mutually independent from the known set of thirty-three in total classical invariants. In the special case of polynomial invariants, this result paves the way for identification of a corresponding minimal integrity basis.

Citation

Soldatos, K. P., Shariff, M. H. B. M., & Merodio, J. (2021). On the constitution of polar fiber-reinforced materials. Mechanics of Advanced Materials and Structures, 28(21), 2255-2266. https://doi.org/10.1080/15376494.2020.1729449

• Journal Article Type: Article
• Acceptance Date: Feb 10, 2020
• Online Publication Date: Mar 2, 2020
• Publication Date: 2021
• Deposit Date: Feb 19, 2020
• Publicly Available Date: Mar 3, 2021
• Journal: Mechanics of Advanced Materials and Structures
• Print ISSN: 1537-6494
• Electronic ISSN: 1537-6532
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 21
• Pages: 2255-2266
• DOI: https://doi.org/10.1080/15376494.2020.1729449
• Keywords: Cosserat elasticity; Fibre-reinforced materials; Fibres resistant in bending; Polar hyperelasticity; Polar elasticity; Spectral invariants; Weak discontinuity surfaces; Mechanical Engineering; General Materials Science; Mechanics of Materials; General Mat
• Public URL: https://nottingham-repository.worktribe.com/output/3993811
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/15376494.2020.1729449