Related papers: Isometric Incompatibility in Growing Elastic Sheet…
Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. Previous research identified the origin of the frustration as the violation of Gauss's \emph{Theorema Egregium}.…
We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate non-zero Gaussian curvature up to size scales that ultimately vanish with their elastic…
The incompatibility of linearized piecewise smooth strain field, arising out of volumetric and surface densities of topological defects and metric anomalies, is investigated. First, general forms of compatibility equations are derived for a…
We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…
If an inextensible thin sheet is adhered to a substrate with a negative Gaussian curvature it will experience stress due to geometric frustration. We analyze the consequences of such geometric frustration using analytic arguments and…
Geometrically frustrated solids with non-Euclidean reference metric are ubiquitous in biology and are becoming increasingly relevant in technological applications. Often they acquire a targeted con- figuration of incompatibility through…
Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large…
Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…
The elastic response of the crystalline sheet to the stretching deformation in the form of wrinkles has been extensively investigated. In this work, we extend this fundamental scientific question to the plastic regime by exploring the…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list…
Programming the non-uniform growth of a responsive polymer gel has emerged as a powerful tool to shape sheets into prescribed three dimensional shapes. We demonstrate that shapes with zero Gaussian curvature, except at singularities,…
Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined…
The interplay between geometry, topology and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this commentary we show how frustration in this context can result in the faceting…
Ribbons are elastic bodies of thickness $t$ and width $w$ with $t\ll w\ll 1$ (after appropriate nondimensionalization). Many ribbons in nature have a non-trivial internal geometry, making them incompatible with Euclidean space. This…
Geometric frustration arises when lattice structure prevents simultaneous minimization of local interactions. It leads to highly degenerate ground states and, subsequently, complex phases of matter such as water ice, spin ice and frustrated…
Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either non-cumulative, which implies an extensive…
The uniform director field obtained for the nematic ground state of the hard-rod model of liquid crystals in two dimensions reflects the high symmetry of the constituents of the liquid; It is a manifestation of the constituents' local…
Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current…
We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause…