Abstract
This paper presents a closed-form expression for the homogenized longitudinal shear moduli of a linear elastic composite material reinforced by long, parallel, radially-graded circular fibres with a periodic arrangement. An imperfect linear elastic fibre-matrix interface is allowed. The asymptotic homogenization method is adopted, and the relevant cell problem is addressed. Periodicity is enforced by resorting to the theory of Weierstrass elliptic functions. The equilibrium equation in the fibre domain is solved in closed form by applying the theory of hypergeometric functions, for new wide classes of grading profiles defined in terms of special functions. The effectiveness of the present analytical procedure is proved by convergence analysis and comparison with finite element solutions. A parametric analysis investigating the influence of microstructural and material features on the effective moduli is presented. The feasibility of mitigating the shear stress concentration in the composite by tuning the fibre grading profile is shown.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.