Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness – Part II: determination of the spherical part of the couple-stress

Soldatos, K. P.

Abstract

The indeterminacy of the spherical part of couple-stress is a well-known drawback of any theoretical formulation stemming from the Cosserat couple-stress theory of elasticity. The relevant theory of finite elastic deformations of solids reinforced by a family of fibres that resist bending is not an exception. The present communication extends and completes that theory in a manner that enables it to measure the spherical part of the couple-stress tensor outside the conventional equilibrium considerations. To achieve this, the present study reconsiders an extra piece of information that has surprisingly emerged already but, so far, has been left unexplained and unexploited; namely, the fact that the energy stored in a fibrous composite elastic solid with fibre-bending stiffness involves a couple-stress generated term that does not influence the relevant couple-stress constitutive equation. The thus resulting new theoretical development complements the theory previously presented without dismissing any of the theoretical results detailed or the conclusions drawn there. Its validity embraces boundary value problems concerning both finite and infinitesimal elastic deformations of polar fibrous composites. In the latter case, its applicability is also tested and verified through the successful determination of the spherical couple-stress of a polar transversely isotropic elastic plate subjected to pure bending.

Citation

Soldatos, K. P. (2023). Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness – Part II: determination of the spherical part of the couple-stress. Mathematics and Mechanics of Solids, 28(1), 124-140. https://doi.org/10.1177/10812865211061595

• Journal Article Type: Article
• Acceptance Date: Nov 3, 2021
• Online Publication Date: Dec 27, 2021
• Publication Date: 2023-01
• Deposit Date: Nov 5, 2021
• Publicly Available Date: Nov 5, 2021
• Journal: Mathematics and Mechanics of Solids
• Print ISSN: 1081-2865
• Electronic ISSN: 1741-3028
• Publisher: SAGE Publications
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 1
• Pages: 124-140
• DOI: https://doi.org/10.1177/10812865211061595
• Keywords: Couple-stress theory; Elasticity; Fibre-reinforced solids; Fibres resistant in bending; Generalised Cosserat theory; Polar elasticity; Spherical part of the couple-stress
• Public URL: https://nottingham-repository.worktribe.com/output/6612813
• Publisher URL: https://journals.sagepub.com/doi/10.1177/10812865211061595
• Additional Information: Accepted for publication in "Mathematics and Mechanics of Solids" on 03 November 2021