Asymptotic study of geometrically non-linear elastic strip with regular system of fibres

Two-dimensional composite material consisting of linear elastic fibres embedded in a non-linear elastic strip has been studied. That inhomogeneous medium models a mechanical behaviour of a rubber-like textile reinforced with threads distributed in parallel. The analytical solution relating the displacement field to fibre width, fibre distance, fibre length and fibre and matrix elastic moduli has been derived. To this end we used a special perturbation and homogenization technique. Anlustrative example is also provided.