English
Related papers

Related papers: Pattern selection and multiscale behavior in metri…

200 papers

Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not…

Soft Condensed Matter · Physics 2009-05-29 Efi Efrati , Eran Sharon , Raz Kupferman

We show that nonlinearly elastic plates of thickness $h\to 0$ with an $\varepsilon$-periodic structure such that $\varepsilon^{-2}h\to 0$ exhibit non-standard behaviour in the asymptotic two-dimensional reduction from three-dimensional…

Analysis of PDEs · Mathematics 2015-11-19 Mikhail Cherdantsev , Kirill Cherednichenko

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…

Soft Condensed Matter · Physics 2009-11-13 Efi Efrati , Eran Sharon , Raz Kupferman

We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic…

Optimization and Control · Mathematics 2015-06-04 John Gemmer , Shankar Venkataramani

We consider a thin elastic sheet in the shape of a disk whose reference metric is that of a singular cone. I.e., the reference metric is flat away from the center and has a defect there. We define a geometrically fully nonlinear free…

Analysis of PDEs · Mathematics 2016-03-23 Heiner Olbermann

A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…

Soft Condensed Matter · Physics 2020-12-08 Yipin Su , Ray W. Ogden , Michel Destrade

The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal…

Analysis of PDEs · Mathematics 2009-01-27 Maria Giovanna Mora , Lucia Scardia

The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…

Analysis of PDEs · Mathematics 2023-01-18 Klaus Böhnlein , Stefan Neukamm , David Padilla-Garza , Oliver Sander

The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian…

Soft Condensed Matter · Physics 2015-07-10 John Gemmer , Eran Sharon , Shankar Venkataramani

Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…

Soft Condensed Matter · Physics 2016-04-12 Jingchen Feng , Herbert Levine , Xiaoming Mao , Leonard M. Sander

We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…

Soft Condensed Matter · Physics 2017-06-08 Matteo Pezzulla , Norbert Stoop , Xin Jiang , Douglas P. Holmes

We consider a geometrically fully nonlinear variational model for thin elastic sheets that contain a single disclination. The free elastic energy contains the thickness $h$ as a small parameter. We give an improvement of a recently proved…

Analysis of PDEs · Mathematics 2018-04-18 Heiner Olbermann

Liquid crystal elastomers (LCEs) marry the large deformation response of a cross-linked polymer network with the nematic order of liquid crystals pendent to the network. Of particular interest is the actuation of LCE sheets where the…

Soft Condensed Matter · Physics 2024-10-02 Lucas Bouck , David Padilla-Garza , Paul Plucinsky

We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic…

Soft Condensed Matter · Physics 2009-11-07 Xiangjun Xing , Leo Radzihovsky

We prove a relation between the scaling $h^\beta$ of the elastic energies of shrinking non-Euclidean bodies $S_h$ of thickness $h\to 0$, and the curvature along their mid-surface $S$. This extends and generalizes similar results for plates…

Analysis of PDEs · Mathematics 2019-01-23 Cy Maor , Asaf Shachar

We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodelling develops a rich variety of shapes as a result of a competition between viscous relaxation and activity. In the regime where active processes…

Soft Condensed Matter · Physics 2020-02-26 D. A. Matoz-Fernandez , Fordyce A. Davidson , Nicola R. Stanley-Wall , Rastko Sknepnek

Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components…

Soft Condensed Matter · Physics 2025-07-15 Michele Fossati , Colin Scheibner , Michel Fruchart , Vincenzo Vitelli

Disorder-induced spectral correlations of mesoscopic quantum systems in the non-diffusive regime and their effect on the magnetic susceptibility are studied. We perform impurity averaging for non-translational invariant systems by combining…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 Edward McCann , Klaus Richter

We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…

Analysis of PDEs · Mathematics 2023-03-01 Marin Bužančić , Elisa Davoli , Igor Velčić

Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here we use molecular dynamics (MD) to study the…

Soft Condensed Matter · Physics 2022-06-28 Zhitao Chen , Duanduan Wan , Mark J. Bowick
‹ Prev 1 2 3 10 Next ›