Derivation of a homogenized bending-torsion theory for rods with micro-heterogeneous prestrain
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Publication:2202455
DOI10.1007/s10659-020-09777-6zbMath1447.74024arXiv1903.08290OpenAlexW3031007894MaRDI QIDQ2202455
Publication date: 18 September 2020
Published in: Journal of Elasticity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1903.08290
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Micromechanics of solids (74M25) Composite and mixture properties (74E30) Homogenization in equilibrium problems of solid mechanics (74Q05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
Related Items (2)
A homogenized bending theory for prestrained plates ⋮ A nonlinear bending theory for nematic LCE plates
Cites Work
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- A corrected Sadowsky functional for inextensible elastic ribbons
- Plates with incompatible prestrain
- Derivation of a homogenized nonlinear plate theory from 3d elasticity
- The Monge-Ampère constraint: matching of isometries, density and regularity, and elastic theories of shallow shells
- Shape programming for narrow ribbons of nematic elastomers
- Commutability of homogenization and linearization at identity in finite elasticity and applications
- On the bending and twisting of rods with misfit
- On the commutability of homogenization and linearization in finite elasticity
- Non-periodic homogenization of bending-torsion theory for inextensible rods from 3D elasticity
- Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
- Elastic theory of unconstrained non-Euclidean plates
- Two-scale convergence of some integral functionals
- Derivation of a homogenized von-Kármán shell theory from 3D elasticity
- A variational justification of linear elasticity with residual stress
- Intrinsic methods in elasticity: a mathematical survey
- Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity
- Ordinary differential equations of non-linear elasticity. I: Foundations of the theories of non-linearly elastic rods and shells
- Derivation of the nonlinear bending-torsion theory for inextensible rods by \(\Gamma\)-convergence
- Linearized elasticity as \(\Gamma\)-limit of finite elasticity
- Regularity of intrinsically convex \(W^{2,2}\) surfaces and a derivation of a homogenized bending theory of convex shells
- Plates with incompatible prestrain of high order
- Actuation of thin nematic elastomer sheets with controlled heterogeneity
- Rigorous derivation of a homogenized bending-torsion theory for inextensible rods from three-dimensional elasticity
- Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models
- A Riemannian approach to reduced plate, shell, and rod theories
- On the derivation of homogenized bending plate model
- Homogenization of the nonlinear bending theory for plates
- Plate theory for stressed heterogeneous multilayers of finite bending energy
- Minimal energy configurations of strained multi-layers
- On global and local minimizers of prestrained thin elastic rods
- Growth and instability in elastic tissues
- On the role of curvature in the elastic energy of non-Euclidean thin bodies
- A Variational Model for Anisotropic and Naturally Twisted Ribbons
- Periodically wrinkled plate model of the Föppl-von Kármán type
- DERIVATION OF A HOMOGENIZED VON-KÁRMÁN PLATE THEORY FROM 3D NONLINEAR ELASTICITY
- 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 theW2,2isometric immersions of Riemannian metrics
- Finite element simulation of nonlinear bending models for thin elastic rods and plates
- Homogenization and Two-Scale Convergence
- A General Convergence Result for a Functional Related to the Theory of Homogenization
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
- Rigorous derivation of active plate models for thin sheets of nematic elastomers
- Dimension Reduction for Thin Films with Transversally Varying Prestrain: Oscillatory and Nonoscillatory Cases
- The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity
- Elastic-Plastic Deformation at Finite Strains
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