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When subjected to specific prestresses, continuum elastic shells can exhibit geometric zero modes: complex motions that require vanishing elastic energy to excite, enabling them to be driven by weak and generic energy inputs. Despite recent…
The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the…
In this paper we study the asymptotic behavior of a structure made of curved rods of thickness 2\delta when \delta rightarrow 0. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…
Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry,…
The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework…
In this work, we study the mechanics of metamaterial sheets inspired by the pellicle of Euglenids. They are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of…
In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic order parameters. Reduced energy functionals are deduced…
We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate…
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…
We study the equilibrium and near-equilibrium properties of a holographic five-dimensional model consisting of Einstein gravity coupled to a scalar field with a non-trivial potential. The dual four-dimensional gauge theory is not conformal…
We show that, at low temperatures, macroscopic inhomogeneities of the electron density in the interior of a finite sample cause a reduction in the measured conductivity peak heights $\sigma_{xx}^{\rm max}$ compared to the universal values…
Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead…
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…
Nanoscale molecular transport plays a crucial role in regulating mass diffusion and responsiveness in condensed matter systems. In soft porous crystals, in particular, adsorption of guest molecules induces host framework deformation and…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
We study the sedimentation of colloidal gels by using a combination of light scattering, polarimetry and video imaging. The asymptotic concentration profiles $\varphi(z,t\rightarrow \infty)$ exhibit remarkable scaling properties: profiles…
Using continuum elasticity theory, we describe the elastic behavior of helical coils with an asymmetric double-helix structure and identify conditions, under which they become very rigid. Theoretical insight gained for macro-structures…
The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four…