  Honeycomb-like microstructures have been shown to exhibit local elastic
buckling under compression, with three possible geometric buckling modes, or
pattern transformations. The individual pattern transformations, and
consequently also spatially distributed patterns, can be induced by controlling
the applied compression along two orthogonal directions. Exploitation of this
property holds great potential in, e.g., soft robotics applications. For fast
and optimal design, efficient numerical tools are required, capable of bridging
the gap between the microstructural and engineering scale, while capturing all
relevant pattern transformations. A micromorphic homogenization framework for
materials exhibiting multiple pattern transformations is therefore presented in
this paper, which extends the micromorphic scheme of Roko\v{s} et al., J. Mech.
Phys. Solids 123, 119-137 (2019), for elastomeric metamaterials exhibiting only
a single pattern transformation. The methodology is based on a suitable
kinematic ansatz consisting of a smooth part, a set of spatially correlated
fluctuating fields, and a remaining, spatially uncorrelated microfluctuation
field. Whereas the latter field is neglected or condensed out at the level of
each macroscopic material point, the magnitudes of the spatially correlated
fluctuating fields emerge at the macroscale as micromorphic fields. We develop
the balance equations which these micromorphic fields must satisfy as well as a
computational homogenization approach to compute the generalized stresses
featuring in these equations. To demonstrate the potential of the methodology,
loading cases resulting in mixed modes in both space and time are studied and
compared against full-scale simulations. It is shown that the proposed
framework is capable of capturing the relevant phenomena, although the inherent
multiplicity of solutions entails sensitivity to the initial guess.
