  We investigate the shear elastic modulus of soft polymer foams loaded with
hard spherical particles and we show that, for constant bubble size and gas
volume fraction, strengthening is strongly dependent on the size of those
inclusions. Through an accurate control of the ratio $\lambda$ that compares
the particle size to the thickness of the struts in the foam structure, we
evidence a transition in the mechanical behavior at $\lambda \approx 1$. For
$\lambda < 1$, every particle loading leads to a strengthening effect whose
magnitude depends only on the particle volume fraction. On the contrary, for
$\lambda > 1$, the strengthening effect weakens abruptly as a function of
$\lambda$ and a softening effect is even observed for $\lambda \gtrsim 10$.
This transition in the mechanical behavior is reminiscent of the so-called
"particle exclusion transition" that has been recently reported within the
framework of drainage of foamy granular suspensions [Haffner B, Khidas Y,
Pitois O. The drainage of foamy granular suspensions. J Colloid Interface Sci
2015. In Press.]. It involves the evolution for the geometrical configuration
of the particles with respect to the foam network, and it appears to control
the mechanics of such foamy systems.
