Mathematical Problems in Thin Elastic Sheets: Scaling Limits, Packing, Crumpling and Singularities

DOI10.1007/978-3-319-54514-1_3zbMath1372.35003OpenAlexW2617256353MaRDI QIDQ5282938

Stefan Müller

Publication date: 17 July 2017

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-54514-1_3

zbMATH Keywords

nonlinear plate theoryvariational toolselastic objectsKármán's theory

Mathematics Subject Classification ID

Related Items (9)

Curvature-driven wrinkling of thin elastic shells ⋮ The time-dependent von Kármán shell equation as a limit of three-dimensional nonlinear elasticity ⋮ The asymptotically sharp geometric rigidity interpolation estimate in thin bi-Lipschitz domains ⋮ On the bending and twisting of rods with misfit ⋮ Distributed branch points and the shape of elastic surfaces with constant negative curvature ⋮ On the Korn Interpolation and Second Inequalities in Thin Domains ⋮ Weighted asymptotic Korn and interpolation Korn inequalities with singular weights ⋮ A hierarchy of multilayered plate models ⋮ A hint on the localization of the buckling deformation at vanishing curvature points on thin elliptic shells

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Energy scaling law for the regular cone
• Limits of elastic models of converging Riemannian manifolds
• Plates with incompatible prestrain
• Energy scaling laws for conically constrained thin elastic sheets
• Metric-induced wrinkling of a thin elastic sheet
• Variational models for prestrained plates with Monge-Ampère constraint.
• Energy scaling law for a single disclination in a thin elastic sheet
• The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity
• Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density
• Energy bounds for a compressed elastic film on a substrate
• Approximation of flat \(W ^{2,2}\) isometric immersions by smooth ones
• The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
• A variational definition of the strain energy for an elastic string
• Optimal rigidity estimates for nearly umbilical surfaces
• Stability of slender bodies under compression and validity of the von Kármán theory
• Elastic theory of unconstrained non-Euclidean plates
• Continuously distributed wrinkles in fabrics
• Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity
• A justification of the von Kármán equations
• New integral estimates for deformations in terms of their nonlinear strains
• Stability estimates in Liouville's theorem and the \(L_p\)-integrability of the derivatives of quasi-conformal mappings
• The morphology and folding patterns of buckling-driven thin-film blisters
• An introduction to \(\Gamma\)-convergence
• On the justification of the nonlinear inextensional plate model
• Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
• Justification of the nonlinear Kirchhoff-Love theory of plates as the application of a new singular inverse method
• Derivation of the nonlinear bending-torsion theory for inextensible rods by \(\Gamma\)-convergence
• On the Sobolev space of isometric immersions
• Energy scaling of compressed elastic films -- three-dimensional elasticity and reduced theories
• The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• Korn's second inequality and geometric rigidity with mixed growth conditions
• A Riemannian approach to reduced plate, shell, and rod theories
• Riemann-Cartan geometry of nonlinear dislocation mechanics
• Convergence of equilibria for incompressible elastic plates in the von Kármán regime
• Rigorous derivation of the formula for the buckling load in axially compressed circular cylindrical shells
• Analysis of a compressed thin film bonded to a compliant substrate: the energy scaling law
• Conical singularities in thin elastic sheets
• Confining thin elastic sheets and folding paper
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• A \(C^{0}\) estimate for nearly umbilical surfaces
• Confined structures of least bending energy
• Liouville's theorem on conformal mappings for minimal regularity assumptions
• On the stability of conformal mappings in multidimensional spaces
• The one-dimensional model for \(d\)-cones revisited
• \(C^1\) isometric imbeddings
• Une justification partielle du modèle de plaque en flexion par -convergence
• Energy estimates for the von Kármán model of thin-film blistering
• Prototypical model for tensional wrinkling in thin sheets
• Geometry and mechanics of two-dimensional defects in amorphous materials
• Symmetry breaking in indented elastic cones
• Stress focusing in elastic sheets
• Euler-lagrange equation and regularity for flat minimizers of the Willmore functional
• The Föppl-von Kármán equations for plates with incompatible strains
• Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics
• Large Time Existence for Thin Vibrating Plates
• Some Open Problems in Elasticity
• Rotation and strain
• Rigorous Derivation of Föppl’s Theory for Clamped Elastic Membranes Leads to Relaxation
• Convergence of Equilibria of Thin Elastic Plates - The Von Karman Case
• Convergence of equilibria of three-dimensional thin elastic beams
• The Relaxed Energy Density for Isotropic Elastic Membranes
• Weakly Differentiable Functions
• Lower bounds for the energy in a crumpled elastic sheet—a minimal ridge
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture
• Exact Scaling Exponents in Korn and Korn-Type Inequalities for Cylindrical Shells
• Blister Patterns and Energy Minimization in Compressed Thin Films on Compliant Substrates
• Wrinkles as the Result of Compressive Stresses in an Annular Thin Film
• Almost Conical Deformations of Thin Sheets with Rotational Symmetry
• Confined developable elastic surfaces: cylinders, cones and the Elastica
• Convergence of equilibria for planar thin elastic beams
• The elements of draping
• Nonlinear problems of elasticity
• Rigourous bounds for the Föppl-von Kármán theory of isotropically compressed plates

This page was built for publication: Mathematical Problems in Thin Elastic Sheets: Scaling Limits, Packing, Crumpling and Singularities