Table 4:

Homogenised estimates of the elastic constants of the transversely isotropic LC obtained using different analytical (generalised self-consistent method and Hashin-Shtrikmann upper bound) and numerical (periodic homogenization on hexagonal cell) methods for an isotropic matrix (($E_m=670000\mathrm{P}\mathrm{a}$, ${\nu }_m=0.49$ as in [19]) with cylindrical cavities and porosity $\varphi =0.43$. $E_t$ and ${\mu }_t$ are Young’s and shear moduli in the plane of isotropy of the transverse isotropic homogenised solid. $E_z$, ${\mu }_z$ and ${\nu }_z$ are the Young’s modulus, shear modulus and Poisson ratio in the transverse direction, respectively.

Method	$E_z\left[\mathrm{P}\mathrm{a}\right]$	${\mu }_z\left[\mathrm{P}\mathrm{a}\right]$	${\nu }_z[-]$	$E_t\left[\mathrm{P}\mathrm{a}\right]$	${\mu }_t\left[\mathrm{P}\mathrm{a}\right]$
Generalized Self-consistent,[51]	381900	89618	0.49	175660	59718
Hashin-Shtrikmann (+),[52]	381900	89618	0.49	230963	88553.3
Periodic Homegenization, [49, 50]	381887	89573	0.49	215025	79550.0