Related papers: Topological elasticity of non-orientable ribbons
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, either representing finite material elements or even the molecular bonds of a system. However, to date,…
In this note, we propose a formal framework accounting for the sensitivity of a function of the domain with respect to the addition of a thin ligament. To set ideas, we consider the model setting of elastic structures, and we approximate…
We investigate the possibility of a striped inhomoegenous phase occurring as an electronic system with an order parameter linearly coupled to the elastic degrees of freedom is tuned through the electronic phase transition. We find that in…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented…
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…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
Elastic strips provide a canonical system for studying the mechanisms governing elastic shape transitions. Buckling, linear snap-through, and nonlinear snap-through have been observed in boundary-actuated strips and linked to the type of…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while…
Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…
It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…
Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids -- materials that are energized from within, with elastic response about a well defined reference…
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena…
Natural slender structures, such as plant leaves, petals, and tendrils, often exhibit complex three-dimensional (3D) morphologies-including twisting, helical coiling, and saddle-bending-driven by differential growth. The resulting internal…
We investigate the nucleation, growth, and spatial organization of topological defects with a ribbon shaped elastic sheet which is stretched and twisted. Singularities are found to spontaneously arrange in a triangular lattice in the form…
We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…