Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation

This paper deals with some theoretical and experimental aspects of the behavior of periodic hyperelastic composites. We focus here on composites consisting of an elastomeric matrix periodically reinforced by long fibers. The paper is composed of three parts. The first part deals with the theoretical aspects of compressible behavior. The second-order theory of Ponte Castañeda (J. Mech. Phys. Solids 44 (1996) 827) is considered and extended to periodic microstructures. Comparisons with results obtained by the finite element method show that the composite behavior predicted by the present model is much more accurate for compressible than for incompressible materials. The second part deals with the extension of the method to incompressible behavior. A mixed formulation (displacement-pressure) is used which improves the accuracy of the estimate given by the model. The third part presents experimental results. The composite tested is made of a rubber matrix reinforced by steel wires. Firstly, the matrix behavior is identified with a tensile test and a shear test carried out on homogeneous samples. Secondly, the composite is tested under shearing. The experimentally measured homogenized stress is then compared with the predictions of the model.