Polar domain walls induced by sequential symmetry breaking in frustrated mechanical metamaterials

Frustration hinders ideal local interactions in systems ranging from artificial spin ices with ice rules to mechanical metamaterials featuring regular floppy modes. While geometric frustrations have been known to promote complex ordered patterns in tessellated lattice structures, there is growing interest in global frustrations due to the topologically nontrivial geometry of metamaterials. However, multiferroic orders in globally frustrated metamaterials have remained elusive. Here, we present polar domain walls constrained in flexible mechanical metamaterials with global frustration and sequential symmetry breaking. We showcase that under simple compressive loading, competing interactions in globally frustrated metamaterials give rise to mixed deformations with high-order buckling modes described by an emergent order parameter. Utilizing an elastic mechanism model, we unveil the process of sequential symmetry breaking and capture the formation of polar domain walls exhibiting a chiral distribution within a multi-well potential landscape. We further demonstrate how to eliminate frustration through torsional loading, leading to symmetry restoration. These results provide insights into the intricate interactions between order and frustration, inspiring the modulation of domain walls in macroscopic systems. Elastic structures featuring tessellated rhombuses exhibit instability and heterogeneous patterns under compression. This study reveals how chiral orders emerge and can be suppressed by adjusting mismatches between local deformations and the overall geometry.