Résumé
The periodic homogenisation method is often used to study the behaviour of heterogeneous media, like fibre enforced composites, soils or tissues. In this present work, the method is applied to derive the homogenised behaviour of a one-dimensional elastic heterogeneous medium under non-linear deformations. For the microscopic description of the problem the St. Venant-Kirchhoff model for hyperelastic material is used. An expression corresponding to the homogenised stress at the macroscopic scale is obtained. The model is tested by studying a special case of a heterogeneous medium composed of two materials with constant Young’s moduli. The obtained stress curve represents realistic values. Furthermore, it is shown that different approaches used in the homogenisation process can lead to different results (e.g. linearisation of non-linearities). Therefore, the importance of non-dimensional formulation before homogenisation process is underlined. Finally, an example of numerical computations at the micro- and macroscopic scales is presented. The results are coherent and enabled us to validate the modeling.