Geometry-based control of instability patterns in cellular soft matter

Recent research has shown the potential of rationally designed geometrical features for controlling the functionality of advanced materials. Of particular recent interest has been the use of geometry for controlling the buckling behaviour of soft materials under compression. However, the effects of geometry may be mixed with those of the mechanical properties. In this paper, we present a specific class of 2D cellular soft matter for which the geometry, independent from the mechanical properties of the bulk material, activates the instability pathways of the material, thereby controlling the instability threshold and the instability mode (instability pattern). The geometrical parameters include those characterizing the shape of the voids and the porosity of the cellular solid. A critical strain that solely depends on the geometry controls the transition to instability. Depending on the above-mentioned geometrical parameters, the onset of instability is followed by either symmetric compaction or side buckling. We provide instability maps that relate the geometrical parameters to the critical strain and the instability mode of the presented cellular soft material. These open up the possibility of using geometry for programming the functionalities of materials.