Geometric linearization of theories for incompressible elastic materials and applications
From MaRDI portal
Publication:5164222
DOI10.1142/S0218202521500202zbMath1482.74035arXiv2004.11271OpenAlexW3128631969MaRDI QIDQ5164222
Publication date: 10 November 2021
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.11271
compactnessnonlinear elasticityincompressibilitygamma-convergencegeometrically linear theorynematic elastomer
Nonlinear elasticity (74B20) PDEs in connection with mechanics of deformable solids (35Q74) Equations linearized about a deformed state (small deformations superposed on large) (74B15)
Related Items (5)
Linearization of elasticity models for incompressible materials ⋮ Pressure live loads and the variational derivation of linear elasticity ⋮ 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
- Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications
- \(\Gamma\)-convergence of energies for nematic elastomers in the small strain limit
- From non linear elasticity to linear elasticity with initial stress via \(\Gamma\)-convergence
- Commutability of homogenization and linearization at identity in finite elasticity and applications
- On the commutability of homogenization and linearization in finite elasticity
- Relaxation of multiwell energies in linearized elasticity and applications to nematic elastomers
- A variational justification of linear elasticity with residual stress
- Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory
- Macroscopic response of nematic elastomers via relaxation of a class of \(SO(3)\)-invariant energies
- Biomechanics of soft tissue in cardiovascular systems. Lecture notes for an advanced school on ``Biomechanics of soft tissue, Udine, Italy, September 10--14, 2001
- Linearized elasticity as \(\Gamma\)-limit of finite elasticity
- Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals
- Variational linearization of pure traction problems in incompressible elasticity
- Extending Sobolev functions with partially vanishing traces from locally \(({\epsilon},{\delta})\)-domains and applications to mixed boundary problems
- On the theory of relaxation in nonlinear elasticity with constraints on the determinant
- A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
- On the equations rot\ v\(=g\) and div\ u\(=f\) with zero boundary conditions
- A-Quasiconvexity: Relaxation and Homogenization
- Closure and Commutability Results for $\Gamma$-Limits and the Geometric Linearization and Homogenization of Multiwell Energy Functionals
- An Introduction to the Mathematical Theory of the Navier-Stokes Equations
- Direct Methods in the Theory of Elliptic Equations
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
- A note on relaxation with constraints on the determinant
- Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance
- Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids
- Semicontinuity problems in the calculus of variations
- Direct methods in the calculus of variations
This page was built for publication: Geometric linearization of theories for incompressible elastic materials and applications
