Homogenization of a Nonlinear Fibre-Reinforced Structure with Contact Conditions on the Interface Matrix-Fibres - H. Samadi; M. El Jarroudi (International Journal of Mathematics And its Applications, 2015)
We study the homogenization of a nonlinear problem posed in a fibre-reinforced composite with matrix-fibres interfacial condition depending on a parameter $λ=λ(ε)$, $ε$ being the size of the basic cell. Using $Γ$- convergence methods, three homogenized problems are determined according to the limit of the ratio$ γ =\frac{λ(ε)}{ε}$. The main result is that the effective constitutive relations reveal non-local terms associated with the microscopic interactions between the matrix and the fibers.