A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
From MaRDI portal
Publication:4790285
DOI10.1002/cpa.10048zbMath1021.74024OpenAlexW2105340951MaRDI QIDQ4790285
Richard D. James, Gero Friesecke, Stefan Müller
Publication date: 28 January 2003
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.10048
energy functionalcurvature functionalnonlinear plate theoryrotation matrixgeometric rigidityrigidity estimatethree-dimensional nonlinear elasticity theory
Nonlinear elasticity (74B20) Plates (74K20) Energy minimization in equilibrium problems in solid mechanics (74G65)
Related Items
Brittle fracture in linearly elastic plates, Adiabatic theory for the area-constrained Willmore flow, Mathematical Problems in Thin Elastic Sheets: Scaling Limits, Packing, Crumpling and Singularities, NONLINEARLY ELASTIC THIN PLATE MODELS FOR A CLASS OF OGDEN MATERIALS II: THE BENDING MODEL, Unnamed Item, Unnamed Item, Laplace-Beltrami equation on hypersurfaces and Γ-convergence, Crack Nucleation in Shells with Through-the-Thickness Microstructure, A continuum model for brittle nanowires derived from an atomistic description by \(\Gamma \)-convergence, Sharp interface limit of the Cahn–Hilliard reaction model for lithium-ion batteries, Pressure live loads and the variational derivation of linear elasticity, Linearization for finite plasticity under dislocation-density tensor regularization, Magnetoelastic thin films at large strains, Line-tension limits for line singularities and application to the mixed-growth case, On Korn's first inequality in a Hardy-Sobolev space, A Bending-Torsion Theory for Thin and Ultrathin Rods as a \(\boldsymbol{\Gamma}\)-Limit of Atomistic Models, Convergent FEM for a Membrane Model of Liquid Crystal Polymer Networks, The tapering length of needles in martensite/martensite macrotwins, Homogenization of discrete thin structures, Minimal energy configurations of bilayer plates as a polynomial optimization problem, A Reduced Model for Plates Arising as Low-Energy \(\boldsymbol{\Gamma}\) -Limit in Nonlinear Magnetoelasticity, The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami, The Willmore flow with prescribed isoperimetric ratio, Stability of isometric immersions of hypersurfaces, A nonlinear bending theory for nematic LCE plates, A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions, Quantitative nonlinear homogenization: control of oscillations, One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams, A geometrically nonlinear Cosserat (micropolar) curvy shell model via gamma convergence, Framed curves, ribbons, and parallel transport on the sphere, Brittle membranes in finite elasticity, Two-phase models for elastic membranes with soft inclusions, Specht Triangle Approximation of Large Bending Isometries, A midsurface elasticity model for a thin, nonlinear, gradient elastic plate, Variational modeling of paperboard delamination under bending, Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio, Shell design from planar pre-stressed structures, Numerical Simulation of Inextensible Elastic Ribbons, Shallow-shell models by Γ-convergence, The Sharp $L^p$ Korn Interpolation and Second Inequalities in Thin Domains, Variational Dimension Reduction in Nonlinear Elasticity: A Young Measure Approach, Microscopic Validation of a Variational Model of Epitaxially Strained Crystalline Films, Asymptotic variational analysis of incompressible elastic strings, A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity, DG approach to large bending plate deformations with isometry constraint, Geometric linearization of theories for incompressible elastic materials and applications, Wrinkles as the Result of Compressive Stresses in an Annular Thin Film, Finite Plasticity in $P^\top\!P$. Part II: Quasi-Static Evolution and Linearization, From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions, Junction of elastic plates and beams, Effective energy integral functionals for thin films in the Orlicz–Sobolev space setting, Improved bounds for composites and rigidity of gradient fields, Curl bounds Grad on SO(3), The Viscous Surface Wave Problem with Generalized Surface Energies, Bending of thin periodic plates, Scaling instability in buckling of axially compressed cylindrical shells, Weighted asymptotic Korn and interpolation Korn inequalities with singular weights, On the Existence of Solutions to the Generalized Marguerre-von Kármán Equations, Strain-Gradient Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy with Mixed Growth, Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity, Surface energies arising in microscopic modeling of martensitic transformations, On material optimisation for nonlinearly elastic plates and shells, Scaling in fracture mechanics by Bažant law: From finite to linearized elasticity, Multiscale homogenization in Kirchhoff's nonlinear plate theory, Trace-Free Korn Inequalities in Orlicz Spaces, Lower bounds of optimal exponentials of thickness in geometry rigidity inequality for shells, Existence and linearization for the Souza-Auricchio model at finite strains, Discontinuous Galerkin approach to large bending deformation of a bilayer plate with isometry constraint, Homogenization theory: periodic and beyond. Abstracts from the workshop held March 14--20, 2021 (online meeting), LDG approximation of large deformations of prestrained plates, Recovery of a manifold with boundary and its continuity as a function of its metric tensor, Plate theory for stressed heterogeneous multilayers of finite bending energy, A nonlinear model for inextensible rods as a low energy \(\varGamma\)-limit of three-dimensional nonlinear elasticity, Rotations with constant curl are constant, Finite element approximation of large bending isometries, Junction between a plate and a rod of comparable thickness in nonlinear elasticity, Sharp geometric rigidity of isometries on Heisenberg groups, Junction of a periodic family of elastic rods with a thin plate. II., Minimal energy configurations of strained multi-layers, Linearization of elasticity models for incompressible materials, Convergence of thin vibrating rods to a linear beam equation, Dimension reduction through gamma convergence for general prestrained thin elastic sheets, A nonlinear Korn inequality based on the Green-Saint Venant strain tensor, Editorial: Variational models in elasticity, An atomistic derivation of von-Kármán plate theory, Homogenization of layered materials with rigid components in single-slip finite crystal plasticity, Rigidity estimates for isometric and conformal maps from \(\mathbb{S}^{n-1}\) to \(\mathbb{R}^n\), On global and local minimizers of prestrained thin elastic rods, Asymptotic behavior of structures made of straight rods, Relative bending energy for weakly prestrained shells, Plasticity as the \(\Gamma\)-limit of a two-dimensional dislocation energy: the critical regime without the assumption of well-separateness, Rigorous derivation of a homogenized bending-torsion theory for inextensible rods from three-dimensional elasticity, Dimension reduction via \(\Gamma \)-convergence for soft active materials, Variational linearization of pure traction problems in incompressible elasticity, Modeling and simulation of thermally actuated bilayer plates, Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells, Derivation of the linear elastic string model from three-dimensional elasticity, Derivation of a homogenized bending-torsion theory for rods with micro-heterogeneous prestrain, The asymptotically sharp geometric rigidity interpolation estimate in thin bi-Lipschitz domains, Actuation of thin nematic elastomer sheets with controlled heterogeneity, Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity, A nonlinear Korn inequality in \(\mathbb{R}^n\) with an explicitly bounded constant, Asymptotic behavior for textiles in von-Kármán regime, Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours, On the geometric rigidity interpolation estimate in thin bi-Lipschitz domains, The isotropic Cosserat shell model including terms up to \(O(h^5)\). I: Derivation in matrix notation, A Naghdi type nonlinear model for shells with little regularity, A compactness and structure result for a discrete multi-well problem with \(\mathrm{SO}(n)\) symmetry in arbitrary dimension, Rigidity of a thin domain depends on the curvature, width, and boundary conditions, Uniqueness of equilibrium with sufficiently small strains in finite elasticity, Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models, Confined elasticae and the buckling of cylindrical shells, The shape of low energy configurations of a thin elastic sheet with a single disclination, The asymptotically sharp Korn interpolation and second inequalities for shells, Variational convergence of discrete geometrically-incompatible elastic models, Korn's second inequality and geometric rigidity with mixed growth conditions, Numerical approximation of von Kármán viscoelastic plates, Reshetnyak rigidity for Riemannian manifolds, Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule, A Riemannian approach to reduced plate, shell, and rod theories, Poincaré meets Korn via Maxwell: extending Korn's first inequality to incompatible tensor fields, On variational dimension reduction in structure mechanics, A metric approach to elastic reformations, Incompatible elasticity and the immersion of non-flat Riemannian manifolds in Euclidean space, A new approach to counterexamples to \(L^1\) estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions, On generalized Cosserat-type theories of plates and shells: a short review and bibliography, Strain tensors on hyperbolic surfaces and their applications, Crystallization to the square lattice for a two-body potential, Transformation cloaking in elastic plates, Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals, Quantitative homogenization in nonlinear elasticity for small loads, On the Kirchhoff-Love hypothesis (Revised and Vindicated), BMO and elasticity: Korn's inequality; local uniqueness in tension, Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks, Rigidity of branching microstructures in shape memory alloys, Reference configurations versus optimal rotations: a derivation of linear elasticity from finite elasticity for all traction forces, Phase-field approximation of functionals defined on piecewise-rigid maps, Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions, Asymptotic rigidity of layered structures and its application in homogenization theory, Symmetric div-quasiconvexity and the relaxation of static problems, Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy, Sharp conditions for the linearization of finite elasticity, Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity, A new variational approach to linearization of traction problems in elasticity, Computable constants for Korn's inequalities on Riemannian manifolds, Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons, The gap between linear elasticity and the variational limit of finite elasticity in pure traction problems, Effective results on uniformization and intrinsic GCM spheres in perturbations of Kerr, Linear models of a stiffened plate via \(\Gamma \)-convergence, Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials, Gamma-limit of a model for the elastic energy of an inextensible ribbon, Bending paper and the Möbius strip, Revisiting the \(C^{1, \alpha} h\)-principle for the Monge-Ampère equation, An analysis of crystal cleavage in the passage from atomistic models to continuum theory, Convergence of equilibria for incompressible elastic plates in the von Kármán regime, Asymptotic behavior of constrained local minimizers in finite elasticity, A hint on the localization of the buckling deformation at vanishing curvature points on thin elliptic shells, On the derivation of homogenized bending plate model, Homogenization of the nonlinear bending theory for plates, Nonlinear Korn inequalities in \(\mathbb R^n\), with or without boundary conditions, Limits of density-constrained optimal transport, A highly anisotropic nonlinear elasticity model for vesicles. I: Eulerian formulation, rigidity estimates and vanishing energy limit, A highly anisotropic nonlinear elasticity model for vesicles. II: Derivation of the thin bilayer bending theory, Stationary points of nonlinear plate theories, Asymptotic analysis of microscopic impenetrability constraints for atomistic systems, Asymptotically correct boundary conditions for the higher-order theory of plate bending, Finite Element Approximation of Large-Scale Isometric Deformations of Parametrized Surfaces, NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART I, Asymptotic analysis of deformation behavior in high-contrast fiber-reinforced materials: Rigidity and anisotropy, Energy minimizing twinning with variable volume fraction, for two nonlinear elastic phases with a single rank-one connection, Noether's theorem and the Willmore functional, Lp-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions, On the role of curvature in the elastic energy of non-Euclidean thin bodies, The mathematics of thin structures, On the general homogenization of von Kármán plate equations from three-dimensional nonlinear elasticity, Reduced Theories in Nonlinear Elasticity, From atomistic systems to linearized continuum models for elastic materials with voids, Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations, Γ-convergence: a tool to investigate physical phenomena across scales, A Riemannian approach to the membrane limit in non-Euclidean elasticity, Geometry, analysis, and morphogenesis: Problems and prospects, Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result, Optimal exponentials of thickness in Korn's inequalities for parabolic and elliptic shells, Simulating Self-Avoiding Isometric Plate Bending, The time-dependent von Kármán shell equation as a limit of three-dimensional nonlinear elasticity, A Piecewise Korn Inequality in SBD and Applications to Embedding and Density Results, On the Passage from Nonlinear to Linearized Viscoelasticity, On asymptotic rigidity and continuity problems in nonlinear elasticity on manifolds and hypersurfaces, Design of pre-stressed plate-strips to cover non-developable shells, A homogenized bending theory for prestrained plates, A Korn-type inequality in SBD for functions with small jump sets, Material optimization for nonlinearly elastic planar beams, Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets, On the uniqueness of energy minimizers in finite elasticity, Unnamed Item, Interpenetration of matter in plate theories obtained as Γ-limits, Deriving one-dimensional model of thin elastic rods using gamma convergence, Bilayer Plates: Model Reduction, Γ-Convergent Finite Element Approximation, and Discrete Gradient Flow, Numerical methods for fully nonlinear and related PDEs. Abstracts from the workshop held June 27 -- July 3, 2021 (hybrid meeting), Modeling and simulation of thin sheet folding, On the Dimension Reduction in Prestrained Elasticity (Survey), Symmetry breaking in indented elastic cones, On scaling properties for two-state problems and for a singularly perturbed \(T_3\) structure, A remark on stress of a spatially uniform dislocation density field, Thin Structures With Imposed Metric, Homogenization of a nonlinear elastic fibre-reinforced composite: a second gradient nonlinear elastic material, On singularities of stationary isometric deformations, A Beam—Just a Beam in Linear Plane Bending, A quasistatic evolution model for perfectly plastic plates derived by \(\varGamma\)-convergence, Operator Perturbation Approach for Fourth Order Elliptic Equations with Variable Coefficients, Linear Strain Tensors on Hyperbolic Surfaces and Asymptotic Theories for Thin Shells, Long-range orientational order of random near-lattice hard sphere and hard disk processes, On properness and related properties of quasilinear systems on unbounded domains, Confining thin elastic sheets and folding paper, A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry, Variational problems in the theory of hydroelastic waves, Approximating \(W^{2,2}\) isometric immersions, Qualitative properties of a continuum theory for thin films, NONLINEARLY ELASTIC THIN PLATE MODELS FOR A CLASS OF OGDEN MATERIALS: I, Decompositions of displacements of thin structures, NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART II, A nonlinear Korn inequality on a surface, A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence, ON RIGID AND INFINITESIMAL RIGID DISPLACEMENTS IN THREE-DIMENSIONAL ELASTICITY, MODELING HETEROGENEOUS MARTENSITIC WIRES, THE REISSNER–MINDLIN PLATE IS THE Γ-LIMIT OF COSSERAT ELASTICITY, Simple proof of two-well rigidity, Nonlinearly elastic membrane model for heterogeneous shells by using a new double scale variational formulation: A formal asymptotic approach, On the Korn Interpolation and Second Inequalities in Thin Domains, On a model of a flexural prestressed shell, Plate theory as the variational limit of the complementary energy functionals of inhomogeneous anisotropic linearly elastic bodies, From finite to linear elastic fracture mechanics by scaling, Spatial heterogeneity in 3D-2D dimensional reduction, A Two Well Liouville Theorem, Spontaneous breaking of rotational symmetry with arbitrary defects and a rigidity estimate, Willmore surfaces with nonremovable singularities and number of critical levels, Convergence of equilibria for bending-torsion models of rods with inhomogeneities, DECOMPOSITION OF DEFORMATIONS OF THIN RODS: APPLICATION TO NONLINEAR ELASTICITY, Derivation of a linear prestressed elastic rod model from three-dimensional elasticity, MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE, Euler-lagrange equation and regularity for flat minimizers of the Willmore functional, The regularisation of theN-well problem by finite elements and by singular perturbation are scaling equivalent in two dimensions, New estimates of the distance between two surfaces in terms of the distance between their fundamental forms, Derivation of Linear Elasticity for a General Class of Atomistic Energies, Rigorous derivation of active plate models for thin sheets of nematic elastomers, A dynamic evolution model for perfectly plastic plates, A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics, Geometry processing from an elastic perspective, Scaling laws for non-Euclidean plates and theW2,2isometric immersions of Riemannian metrics, Modelling nonlinear hydroelastic waves, AN EVOLUTIONARY ELASTOPLASTIC PLATE MODEL DERIVED VIA Γ-CONVERGENCE, Estimates for the constant in two nonlinear Korn inequalities, Discrete-to-continuum limits of planar disclinations, A hierarchy of multilayered plate models, Continuity in \(H^1\)-norms of surfaces in terms of the \(L^1\)-norms of their fundamental forms, Regularity properties of isometric immersions, Derivation of a Line-Tension Model for Dislocations from a Nonlinear Three-Dimensional Energy: The Case of Quadratic Growth, Continuation of Infinitesimal Bendings on Developable Surfaces and Equilibrium Equations for Nonlinear Bending Theory of Plates, A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus, JUNCTION IN A THIN MULTIDOMAIN FOR A FOURTH ORDER PROBLEM, Theories for incompressible rods: A rigorous derivation via Γ-convergence, DERIVATION OF A HOMOGENIZED VON-KÁRMÁN PLATE THEORY FROM 3D NONLINEAR ELASTICITY, Singular Limit for Reactive Diffusive Transport Through an Array of Thin Channels in case of Critical Diffusivity, Linearized von Kármán theory for incompressible magnetoelastic plates, Asymptotic analysis of a junction of hyperelastic rods, From the classical to the generalized von Kármán and Marguerre--von Kármán equations, An introduction to differential geometry with applications to elasticity, Energy scaling law for the regular cone, Nonlinear Korn inequalities in \(\mathbb R^n\) and immersions in \(W^{2,p}\), \(p>n\), considered as functions of their metric tensors in \(W^{1,p}\), Two-dimensional approximation of thin piezoelectric membrane shells using gamma convergence, A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation, Limits of elastic models of converging Riemannian manifolds, Plates with incompatible prestrain, Stability of slender bodies under compression and validity of the von Kármán theory, Decomposition of shell deformations - asymptotic behavior of the Green-St Venant strain tensor, On the crystallization of 2D hexagonal lattices, A geometric theory of nonlinear morphoelastic shells, Regularity of intrinsically convex \(W^{2,2}\) surfaces and a derivation of a homogenized bending theory of convex shells, Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks, A proof of crystallization in two dimensions, Quasistatic evolution of perfectly plastic shallow shells: a rigorous variational derivation, Geometry of logarithmic strain measures in solid mechanics, Derivation of a rod theory for multiphase materials, On a consistent dynamic finite-strain plate theory and its linearization, Nonlinear Korn inequalities on a hypersurface, On a boundary value problem for conically deformed thin elastic sheets, The von Kármán theory for incompressible elastic shells, On equations of motion of a nonlinear hydroelastic structure, Derivation of a rod theory for biphase materials with dislocations at the interface, On functions whose symmetric part of gradient agree and a generalization of Reshetnyak's compactness theorem, Energy scaling laws for conically constrained thin elastic sheets, Gaussian curvature as an identifier of shell rigidity, Piecewise rigidity, A two-gradient approach for phase transitions in thin films, Derivation of a plate theory for incompressible materials, Plates with incompatible prestrain of high order, Nonlinear estimates for hypersurfaces in terms of their fundamental forms, Stochastic homogenization of the bending plate model, A variational model for dislocations at semi-coherent interfaces, A nonlinear Korn inequality in \(W^{2,p}\), \(p>n\), Nonlinear Korn inequalities, Derivation of a homogenized von-Kármán shell theory from 3D elasticity, An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem, Justification of Koiter's shell model using gamma convergence, Rigidity of pairs of quasiregular mappings whose symmetric part of gradient are close, The div-curl lemma for sequences whose divergence and curl are compact in \(W^{-1,1}\), A nonlinear Korn inequality with boundary conditions and its relation to the existence of minimizers in nonlinear elasticity, Capturing the helical to spiral transitions in thin ribbons of nematic elastomers, On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory., On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity., Nonlinear weakly curved rod by \(\Gamma \)-convergence, A convergence theorem for immersions with \(L^2\)-bounded second fundamental form, Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence., Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density, Second-order analysis for thin structures., On the recovery of a manifold with boundary in \(\mathbb R^n\)., Commutability of homogenization and linearization at identity in finite elasticity and applications, On rigid and infinitesimal rigid displacements in shell theory., Derivation of a homogenized nonlinear plate theory from 3d elasticity, An estimate of the \(H^1\)-norm of deformations in terms of the \(L^1\)-norm of their Cauchy-Green tensors, The line-tension approximation as the dilute limit of linear-elastic dislocations, Face-centered cubic crystallization of atomistic configurations, Analysis aspects of Willmore surfaces, The Monge-Ampère constraint: matching of isometries, density and regularity, and elastic theories of shallow shells, Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires, Integral representation for functionals defined on \(SBD^p\) in dimension two, Phase field models for thin elastic structures with topological constraint, Crystallization for a Brenner-like potential, Derivation of homogenized Euler-Lagrange equations for von Kármán rods, On the bending and twisting of rods with misfit, Sharp bounds for geometric rigidity of isometries on Heisenberg groups, Sobolev spaces of isometric immersions of arbitrary dimension and co-dimension, A short note on the derivation of the elastic von Kármán shell theory, Recovery of immersions from their metric tensors and nonlinear Korn inequalities: a brief survey, Energy scaling law for a single disclination in a thin elastic sheet, Shape programming for narrow ribbons of nematic elastomers, On the effect of interactions beyond nearest neighbours on non-convex lattice systems, A derivation of linearized Griffith energies from nonlinear models, The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity, The uniform Korn-Poincaré inequality in thin domains, The Föppl-von Kármán plate theory as a low energy \(\Gamma\)-limit of nonlinear elasticity, Integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions, Some results about the existence of critical points for the Willmore functional, A variational justification of linear elasticity with residual stress, Linear elasticity obtained from finite elasticity by \(\Gamma \)-convergence under weak coerciveness conditions, Quasiconformal frames, On the commutability of homogenization and linearization in finite elasticity, Invertibility and non-invertibility in thin elastic structures, 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, Decomposition of the deformations of a thin shell. Asymptotic behavior of the Green-St Venant's strain tensor, On the passage from atomic to continuum theory for thin films, A nonlinear theory for shells with slowly varying thickness, Non-periodic homogenization of bending-torsion theory for inextensible rods from 3D elasticity, Microstructures in low-hysteresis shape memory alloys: scaling regimes and optimal needle shapes, Homogenization of bending theory for plates; the case of oscillations in the direction of thickness, Modeling the behavior of heat-shrinkable thin films, \(\Gamma \)-convergence for incompressible elastic plates, The flip side of buckling, Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory, Minimizers of Kirchhoff's plate functional: Euler-Lagrange equations and regularity, Rigidity of a non-elliptic differential inclusion related to the Aviles-giga conjecture, Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity, On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime, Self-similar folding patterns and energy scaling in compressed elastic sheets
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- New integral estimates for deformations in terms of their nonlinear strains
- A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
- Convexity conditions and existence theorems in nonlinear elasticity
- The morphology and folding patterns of buckling-driven thin-film blisters
- An introduction to \(\Gamma\)-convergence
- Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
- Rigorous derivation of nonlinear plate theory and geometric rigidity
- Existence of surfaces minimizing the Willmore functional
- The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
- The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
- On surfaces of finite total curvature
- A theory of thin films of martensitic materials with applications to microactuators
- Energy estimates for the von Kármán model of thin-film blistering
- Rotation and strain
- Uniformly Fat Sets
- 3D-2D asymptotic analysis of an optimal design problem for thin films
- Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
- Uniqueness and maximal regularity for nonlinear elliptic systems of n--Laplace type with measure valued right hand side
- Rigourous bounds for the Föppl-von Kármán theory of isotropically compressed plates