2. Reference solution#
2.1. Calculation method#
According to the general theory of the homogenization of composite materials [bib1], the effective Young’s modules \({E}_{\mathit{xx}}^{\mathit{eff}}\) and \({E}_{\mathit{yy}}^{\mathit{eff}}\) in the directions \(X\) and \(Y\) of a mixture having the form given above, are given by the following formulas:
\(\frac{1}{{E}_{\mathit{xx}}^{\mathit{eff}}}\mathrm{=}\frac{{f}_{1}}{{E}_{1}}+\frac{{f}_{2}}{{E}_{2}}\)
\({E}_{\mathit{yy}}^{\mathit{eff}}\mathrm{=}{f}_{1}{E}_{1}+{f}_{2}{E}_{2}\)
\({f}_{1}\) and \({f}_{2}\) are the volume fractions of each material, in our case:
\({f}_{1}\mathrm{=}{f}_{2}\mathrm{=}0.5\)
2.2. Bibliographical references#
BORNET, T. BRETHEAU and P. GILORMINI: Homogenization in the mechanics of materials (T1). Hermes Science Publications - 2001.