Estimate of the homogenized hyperelastic behavior of periodic fiber-reinforced composites using the second-order procedure

We use the second-order procedure of P. Ponte Castaneda to estimate the hyperelastic behavior of periodic composites. The results obtained for a fiber-reinforced composite show that the accuracy of the homogenized energy estimated using this procedure is excellent in the case of compressible materials and poor in the case of quasi-incompressible materials. Then we develop a new formulation for incompressible materials using a Lagrange multiplier which improves the quality of the estimate given by the procedure. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.