Homogenization of elastic materials reinforced by rigid notched fibres

Abstract

This paper deals with the homogenization of a composite material built with an elastic matrix periodically reinforced by elastic notched fibres. We assume that the Lamé constants in the fibres are highly contrasted with respect to those of the matrix. We derive a class of energy functionals involving additional degrees of freedom implying nonlocal description of localized geometrical discontinuities due to the fibre-notches, nonlocal effects associated with thin boundary layer phenomena, and nonlocal terms including macroscopic fields of extension or flexion.

Keywords:

• Elastic matrix
• rigid notched fibres
• homogenization
• nonlocal effects
• nonlocal localized geometrical discontinuities

AMS Subject Classifications:

• 35B27
• 78A48

Notes

No potential conflict of interest was reported by the authors.