1. Reference problem#

1.1. Geometry#

We consider a heterogeneous resin-fiber composite structure that we want to replace by an equivalent homogeneous structure.

The homogenization theory is well suited in such a case because of the periodicity of the glass fibers in the resin. To simplify the problem and thanks to the hypothesis of periodicity, we give ourselves a square base cell in the hexagonal step () and we consider three different geometries where the fiber/resin ratio varies from 0.2 to 0.6.

_images/10000201000002B8000001A84D7050A7AEFD06DD.png

Figure 1.1-1: Fiber/resin ratio equal to 0.2.

 _images/10000201000002AE0000019450A6E4C6993F6336.png

Figure 1.1-2: Fiber/resin ratio equal to 0.4.

 _images/10000201000002AF000001A7CC0E292344E4CCA5.png

Figure 1.1-3: Fiber/resin ratio equal to 0.6.

1.2. Material properties#

The base cell is made of resin and fibreglass. The material parameters are as follows:

Fiberglass:

\(\begin{array}{c}E\text{=}70000\mathit{MPa}\hfill \\ \mathrm{\nu }\text{=}0.22\hfill \\ k\text{=}1.0W/(m\mathrm{.}°C)\hfill \\ {C}_{p}\text{=}0J/(°C\mathrm{.}{m}^{3})\hfill \end{array}\)

Resin:

\(\begin{array}{c}E\text{=}3500\mathit{MPa}\hfill \\ \mathrm{\nu }\text{=}0.35\hfill \\ k\text{=}1.0W/(m\mathrm{.}°C)\hfill \\ {C}_{p}\text{=}0J/(°C\mathrm{.}{m}^{3})\hfill \end{array}\)