Variational linearization of pure traction problems in incompressible elasticity
From MaRDI portal
Publication:2198140
DOI10.1007/s00033-020-01377-7zbMath1447.74007arXiv2005.14697OpenAlexW3081771195MaRDI QIDQ2198140
Danilo Percivale, Edoardo Mainini
Publication date: 9 September 2020
Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.14697
Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) PDEs in connection with mechanics of deformable solids (35Q74) Equations linearized about a deformed state (small deformations superposed on large) (74B15)
Related Items (9)
Linearization of elasticity models for incompressible materials ⋮ Pressure live loads and the variational derivation of linear elasticity ⋮ A stabilized nonconforming Crouzeix–Raviart finite element method for the elasticity eigenvalue problem with the pure traction boundary condition ⋮ Asymptotic variational analysis of incompressible elastic strings ⋮ Geometric linearization of theories for incompressible elastic materials and applications ⋮ Reference configurations versus optimal rotations: a derivation of linear elasticity from finite elasticity for all traction forces ⋮ Sharp conditions for the linearization of finite elasticity ⋮ Asymptotic behavior of constrained local minimizers in finite elasticity ⋮ Nonlinear and linearized models in thermoviscoelasticity
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar's data
- A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
- Linear elasticity obtained from finite elasticity by \(\Gamma \)-convergence under weak coerciveness conditions
- Stability of slender bodies under compression and validity of the von Kármán theory
- Mechanical models of artery walls
- \(\Gamma \)-convergence for incompressible elastic plates
- Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory
- From SBD to SBH: The elastic-plastic plate
- Linearized elasticity as \(\Gamma\)-limit of finite elasticity
- Shape variation and optimization. A geometrical analysis
- Smooth and broken minimizers of some free discontinuity problems
- Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals
- An introduction to continuum mechanics
- A new variational approach to linearization of traction problems in elasticity
- The gap between linear elasticity and the variational limit of finite elasticity in pure traction problems
- A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
- On the validation of theories of thin elastic structures
- Closure and Commutability Results for $\Gamma$-Limits and the Geometric Linearization and Homogenization of Multiwell Energy Functionals
- A VARIATIONAL PRINCIPLE FOR PLASTIC HINGES IN A BEAM
- On Korn's second inequality
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
- From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions
- Extension and representation of divergence-free vector fields on bounded domains
This page was built for publication: Variational linearization of pure traction problems in incompressible elasticity
