Related papers: Shape programming for narrow ribbons of nematic el…
Experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [Y. Klein, E. Efrati, and E. Sharon, Science…
We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…
Taking advantage of the competition between elasticity and capillarity has proven to be an efficient way to design structures by folding, bending, or assembling elastic objects in contact with liquid interfaces. Elastocapillary effects…
We compare six elastic models for polymer networks in the context of phase separation within a gel, including a new model that combines the finite extensible Arruda-Boyce model and the slip tube model for entangled chains. We study…
The problem of determining three-dimensional density fields from single two-dimensional projections is hopelessly underdetermined without additional assumptions. While parameterized inversions are typically used to solve this problem, we…
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,…
From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form…
Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling…
We study ribbons of vanishing Gaussian curvature, i.e., flat ribbons, constructed along a curve in $\mathbb{R}^{3}$. In particular, we first investigate to which extent the ruled structure determines a flat ribbon: in other words, we ask…
Graphene nanoribbons are the flimsiest material systems in the world, and they get readily distorted. Distortion by twisting, for one, is important because it couples to ribbon's electronic properties. In this Letter, using simulations with…
We study the equilibria of a photoresponsive nematic elastomer ribbon within a continuum theory that builds upon the statistical mechanics model put forward by Corbett and Warner [Phys. Rev. E 78, 061701 (2008)]. We prove that the…
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…
A rate-independent model for the quasistatic evolution of a magnetoelastic thin film is advanced and analyzed. Starting from the three-dimensional setting, we present an evolutionary $\Gamma$-convergence argument in order to pass to the…
Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to…
In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat…
We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in…
Thin elastic films can spontaneously attach to liquid interfaces, offering a platform for tailoring their physical, chemical, and optical properties. Current understanding of the elastocapillarity of thin films is based primarily on studies…
We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also…
In this paper we investigate rods made of nonlinearly elastic, composite--materials that feature a micro-heterogeneous prestrain that oscillates (locally periodic) on a scale that is small compared to the length of the rod. As a main result…
This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the…