, of Minnesota through NSF grants PHY-0941493 and CMMI-1462826 and the LMS at the Ecole Polytechnique during two consecutive, one-year post-doctoral fellowships in each Institution. The work of R. E. was supported by the NSF grants PHY-0941493 and CMMI-1462826 and by the LMS during several short visits. The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources

K. Bertoldi, M. Boyce, S. Deschanel, S. Prange, and T. Mullin, Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures, J. Mech. Phys. Solids, vol.56, pp.2642-2668, 2008.

C. J. Combescure, P. Henry, and R. S. Elliott, Post-bifurcation and stability of a finitely strained hexagonal honeycomb subjected to equi-biaxial in-plane loading, International Journal of Solids and Structures, vol.88, pp.296-318, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01647871

R. S. Elliott, J. A. Shaw, and N. Triantafyllidis, Stability of crystalline solids-II: Application to temperature-induced martensitic phase transformations in bi-atomic crystals, Journal of the Mechanics and Physics of Solids, vol.54, pp.193-232, 2006.

R. S. Elliott, N. Triantafyllidis, and J. A. Shaw, Reversible stress-induced martensitic phase transformations in a bi-atomic crystal, Journal of the Mechanics and Physics of Solids, vol.59, pp.216-236, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00544469

M. Golublitsky, I. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Applied Mathematical Sciences, vol.2, 1988.

B. Haghpanah, J. Papadopoulos, D. Mousanezhad, H. Nayeb-hashemi, and A. Vaziri, Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state, Proc. R. Soc. A Math. Phys. Eng. Sci, vol.470, pp.20130856-20130856, 2014.

Y. He, Y. Zhou, Z. Liu, and K. M. Liew, Buckling and pattern transformation of modified periodic lattice structures, Extrem. Mech. Lett, vol.22, pp.112-121, 2018.

J. W. Hutchinson, Plastic buckling, Advances in Applied Mechanics, vol.14, pp.66-143, 1974.

D. Karagiozova and T. Yu, Strain localization in circular honeycombs under in-plane biaxial quasi-static and low-velocity impact loading, Int. J. Impact Eng, vol.35, pp.753-770, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00499106

R. Mcweeny, Symmetry: An introduction to group theory and its applications, 2002.

J. C. Michel, O. Lopez-pamies, P. Ponte-castañeda, and N. Triantafyllidis, Microscopic and macroscopic instabilities in finitely strained porous elastomers, Journal of the Mechanics and Physics of Solids, vol.55, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00106306

N. Ohno, D. Okumura, and T. Niikawa, Long-wave buckling of elastic square honeycombs subject to in-plane biaxial compression, Int. J. Mech. Sci, vol.46, pp.1697-1713, 2004.

D. Okumura, N. Ohno, and H. Noguchi, Post-buckling analysis of elastic honeycombs subject to in-plane biaxial compression, International journal of solids and structures, vol.39, pp.3487-3503, 2002.

J. T. Overvelde, S. Shan, and K. Bertoldi, Compaction through buckling in 2D periodic, soft and porous structures: Effect of pore shape, Adv. Mater, vol.24, pp.2337-2342, 2012.

J. T. Overvelde and K. Bertoldi, Relating pore shape to the non-linear response of periodic elastomeric structures, J. Mech. Phys. Solids, vol.64, pp.351-366, 2014.

S. Papka and S. Kyriakides, Biaxial crushing of honeycombs:-part 1: Experiments, International Journal of Solids and Structures, vol.36, pp.4367-4396, 1999.

S. Papka and S. Kyriakides, In-plane biaxial crushing of honeycombs?: Part ii, Analysis. International Journal of Solids and Structures, vol.36, pp.4397-4423, 1999.

I. Saiki, K. Ikeda, and K. Murota, Flower patterns appearing on a honeycomb structure and their bifurcation mechanism, International Journal of Bifurcation and Chaos, vol.15, pp.497-515, 2005.

V. Sorkin, R. S. Elliott, and E. B. Tadmor, A local quasicontinuum method for 3d multilattice crystalline materials: Application to shape-memory alloys, Modelling and Simulation in Materials Science and Engineering, vol.22, p.55001, 2014.

J. U. Surjadi, L. Gao, H. Du, X. Li, X. Xiong et al., Mechanical metamaterials and their engineering applications, Adv. Eng. Mater, vol.21, pp.1-37, 2019.

N. Triantafyllidis and R. Peek, On stability and the worst imperfection shape in solids with nearly simultaneous eigenmodes, International Journal of Solids and Structures, vol.29, pp.2281-2299, 1992.

N. Triantafyllidis and S. K. Samanta, Bending effects on flow localization in metallic sheets, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.406, pp.205-226, 1986.

N. Triantafyllidis and M. Schraad, Onset of failure in aluminum honeycombs under general in-plane loading, Journal of the Mechanics and Physics of Solids, vol.46, pp.1089-1124, 1998.