Related papers: Isometric Incompatibility in Growing Elastic Sheet…
Motivated by recent interest in elastic problems in which the target space is non-Euclidean, we study a limit where local rest distances within an elastic body are incompatible, yet close to, distances within the ambient space.…
Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper…
When thermal energies are weak, two dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We…
We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth arouses residual stresses that lead to delamination. This instability can be…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
The inelastic incompressibility is a typical feature of metal plasticity/viscoplasticity. Over the last decade, there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve…
Geometric frustration describes the inability of a local molecular arrangement, such as icosahedra found in metallic glasses and in model atomic glass-formers, to tile space. Local icosahedral order however is strongly frustrated in…
Morphogenesis, the process of growth and shape formation in biological tissues, is driven by complex interactions between mechanical, biochemical, and genetic factors. Traditional models of biological growth often rely on the concept of…
Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points,…
A flat elastic sheet may contain pointlike conical singularities that carry a metrical "charge" of Gaussian curvature. Adding such elementary defects to a sheet allows one to make many shapes, in a manner broadly analogous to the familiar…
Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibers by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral…
Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial…
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…
Disclinations in a 2D sheet create regions of Gaussian curvature whose inversion produces a reconfigurable surface with many distinct metastable shapes, as shown by molecular dynamics of a disclinated graphene monolayer. This material has a…
We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian…
Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can…
We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local…
In this paper we prove some geometric inequalities for closed surfaces in Euclidean three-space. Motivated by Gage's inequality for convex curves, we first verify that for convex surfaces the Willmore energy is bounded below by some…
While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial…