  Rubber blends are ubiquitous in countless technological applications. More
often than not, rubber blends exhibit complex interpenetrating microstructures,
which are thought to have a significant impact on their resulting macroscopic
mechanical properties. As a first step to understand this potential impact,
this paper presents a bottom-up or homogenization study of the nonlinear
elastic response of the prominent class of bicontinuous rubber blends, that is,
blends made of two immiscible constituents or phases segregated into an
interpenetrating network of two separate but fully continuous domains that are
perfectly bonded to one another. The focus is on blends that are isotropic and
that contain an equal volume fraction (50/50) of each phase. The
microstructures of these blends are idealized as microstructures generated by
level cuts of Gaussian random fields that are suitably constrained to be
periodic so as to allow for the construction of unit cells over which periodic
homogenization can be carried out. The homogenized or macroscopic elastic
response of such blends are determined both numerically via finite elements and
analytically via a nonlinear comparison medium method. The numerical approach
makes use of a novel meshing scheme that leads to conforming and periodic
simplicial meshes starting from a voxelized representation of the
microstructures. Results are presented for the fundamental case when both
rubber phases are Neo-Hookean, as well as when they exhibit non-Gaussian
elasticity. Remarkably, irrespective of the elastic behavior of the phases, the
results show that the homogenized response of the blends is largely insensitive
to the specific morphologies of the phases.
