On the role of curvature in the elastic energy of non-Euclidean thin bodies

DOI10.1007/s10659-018-9686-1zbMath1412.74042arXiv1801.02207OpenAlexW2783742761WikidataQ129397314 ScholiaQ129397314MaRDI QIDQ2631830

Cy Maor, Asaf Shachar

Publication date: 16 May 2019

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.02207

zbMATH Keywords

curvaturegamma-convergenceGauss-Codazzi equationsnon-Euclidean platesdimension-reductionincompatible elasticitynon-Euclidean rods

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Plates (74K20) Shells (74K25) Applications of differential geometry to physics (53Z05)

Related Items (8)

Asymptotic rigidity for shells in non-Euclidean elasticity ⋮ Dimension reduction through gamma convergence for general prestrained thin elastic sheets ⋮ Geometry, analysis, and morphogenesis: Problems and prospects ⋮ Stability of isometric immersions of hypersurfaces ⋮ Energy minimising configurations of pre-strained multilayers ⋮ A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions ⋮ Derivation of a homogenized bending-torsion theory for rods with micro-heterogeneous prestrain ⋮ A hierarchy of multilayered plate models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Plates with incompatible prestrain
• Metric-induced wrinkling of a thin elastic sheet
• Energy scaling law for a single disclination in a thin elastic sheet
• On the bending and twisting of rods with misfit
• Elastic theory of unconstrained non-Euclidean plates
• Plates with incompatible prestrain of high order
• Reshetnyak rigidity for Riemannian manifolds
• Incompatible elasticity and the immersion of non-flat Riemannian manifolds in Euclidean space
• The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• A Riemannian approach to reduced plate, shell, and rod theories
• On global and local minimizers of prestrained thin elastic rods
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• A Riemannian approach to the membrane limit in non-Euclidean elasticity
• Symmetry breaking in indented elastic cones
• Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics
• Scaling laws for non-Euclidean plates and theW^2,2isometric immersions of Riemannian metrics
• On isometric immersions of riemannian manifolds
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets
• A geometric theory of thermal stresses

This page was built for publication: On the role of curvature in the elastic energy of non-Euclidean thin bodies