Homogenization of a Nonlinear Fibre-Reinforced Structure with Contact Conditions on the Interface Matrix-Fibres

Abstract

We study the homogenization of a nonlinear problem posed in a fibre-reinforced composite with matrix-fibres interfacial condition depending on a parameter $\lambda=\lambda(\varepsilon)$, $\varepsilon$ being the size of the basic cell. Using $\Gamma$- convergence methods, three homogenized problems are determined according to the limit of the ratio$ \gamma =\frac{\lambda(\varepsilon)}{\varepsilon}$. The main result is that the effective constitutive relations reveal non-local terms associated with the microscopic interactions between the matrix and the fibers.