Related papers: Topological rigidity in twisted, elastic ribbons
Topological magnetic textures confined to two-dimensional (2D) non-orientable manifolds exhibit behaviors absent in planar systems. We investigate bimerons on M\"obius surfaces and show that the lack of global orientation alters…
When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: parity, global…
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…
The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or…
A nematic membrane is a sheet with embedded orientational order, which can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor…
A rich zoology of shapes emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all these shape are not understood, in particular the shape that prevails at large tension and twist and that emerges from a…
This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…
We report an experimental study of the development of orientational order in a crumpled sheet, with a particular focus on the role played by the geometry of confinement. Our experiments are performed on elastomeric sheets immersed in a…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
This review presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing non-trivial textures, focusing in particular on the common motifs of twisted and…
Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these…
Plastic deformation is widely regarded as an intrinsically dissipative phenomenon and its theoretical description is largely phenomenological. We argue instead that plasticity possesses a non-dissipative, symmetry determined backbone:…
Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In…
Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…
Dense rubbery networks are highly entangled polymer systems, with significant topological restrictions for the mobility of neighbouring chains and crosslinks preventing the reptation constraint release. In a mean field approach,…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
Knitting turns yarn, a 1D material, into a 2D fabric that is flexible, durable [1], and can be patterned to adopt a wide range of 3D geometries [2]. Like other mechanical metamaterials [3], the elasticity of knitted fabrics is an emergent…
We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…
We study a topological obstruction of a very stringy nature concerned with deforming the target space of an $N=2$ non-linear \sm. This target space has a singularity which may be smoothed away according to the conventional rules of geometry…
The consolidation of suspended particulate matter under external forces such as pressure or gravity is of widespread interest. In this work, we derive a constitutive relation to describe the deformation of a {\it two-dimensional} strongly…