Dimension reduction through gamma convergence for general prestrained thin elastic sheets

DOI10.1007/S00526-022-02262-ZzbMath1494.49003arXiv2002.07018OpenAlexW4287867274WikidataQ114017858 ScholiaQ114017858MaRDI QIDQ2159519

David Padilla-Garza

Publication date: 1 August 2022

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.07018

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Linear elasticity with initial stresses (74B10) Plates (74K20) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving relations other than differential equations (49J21) Monge-Ampère equations (35J96)

Related Items (3)

A homogenized bending theory for prestrained plates ⋮ A nonlinear bending theory for nematic LCE plates ⋮ A beam model for duoskelion structures derived by asymptotic homogenization and its application to axial loading problems

Cites Work

• Plates with incompatible prestrain
• Convex integration for the Monge-Ampère equation in two dimensions
• Approximation of flat \(W ^{2,2}\) isometric immersions by smooth ones
• Fine level set structure of flat isometric immersions
• The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
• Elastic theory of unconstrained non-Euclidean plates
• Energy minimising configurations of pre-strained multilayers
• A Riemannian approach to reduced plate, shell, and rod theories
• Plate theory for stressed heterogeneous multilayers of finite bending energy
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• On the role of curvature in the elastic energy of non-Euclidean thin bodies
• Curvature-driven wrinkling of thin elastic shells
• Designing Responsive Buckled Surfaces by Halftone Gel Lithography
• High dimensionality and h-principle in PDE
• The Föppl-von Kármán equations for plates with incompatible strains
• Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics
• Scaling laws for non-Euclidean plates and theW^2,2isometric immersions of Riemannian metrics
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity
• Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets
• An asymptotic variational problem modeling a thin elastic sheet on a liquid, lifted at one end
• Dimension Reduction for Thin Films with Transversally Varying Prestrain: Oscillatory and Nonoscillatory Cases

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