Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers
From MaRDI portal
Publication:5107922
DOI10.1051/cocv/2018005zbMath1437.49029arXiv1706.09653OpenAlexW2962774729MaRDI QIDQ5107922
Carlos Mora-Corral, Marcos Oliva
Publication date: 29 April 2020
Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.09653
Nonlinear elasticity (74B20) Methods involving semicontinuity and convergence; relaxation (49J45) Coupling of solid mechanics with other effects (74F99) Manifolds and measure-geometric topics (49Q99)
Related Items (4)
Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers ⋮ Harmonic dipoles and the relaxation of the neo-Hookean energy in 3D elasticity ⋮ \( \Gamma\)-convergence of polyconvex functionals involving \(s\)-fractional gradients to their local counterparts ⋮ Invertibility of Orlicz-Sobolev maps
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence results for incompressible magnetoelasticity
- 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
- A Landau-de Gennes theory of liquid crystal elastomers
- Regularity of inverses of Sobolev deformations with finite surface energy
- Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity
- Fracture surfaces and the regularity of inverses for BV deformations
- Orientability and energy minimization in liquid crystal models
- Quasiconvexity and relaxation of nonconvex problems in the calculus of variations
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Multiple integrals in the calculus of variations
- Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
- Cavitation, invertibility, and convergence of regularized minimizers in nonlinear elasticity
- Fine phase mixtures as minimizers of energy
- Regularity properties of deformations with finite energy
- Null Lagrangians, weak continuity, and variational problems of arbitrary order
- Convexity conditions and existence theorems in nonlinear elasticity
- Macroscopic response of nematic elastomers via relaxation of a class of \(SO(3)\)-invariant energies
- On the existence of minimizers for the neo-Hookean energy in the axisymmetric setting
- Manifold constrained variational problems
- An existence theory for nonlinear elasticity that allows for cavitation
- On a new class of elastic deformations not allowing for cavitation
- On the theory of relaxation in nonlinear elasticity with constraints on the determinant
- The lower quasiconvex envelope of the stored energy function for an elastic crystal
- Ideally soft nematic elastomers
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Relaxation of a model energy for the cubic to tetragonal phase transformation in two dimensions
- Lusin's condition and the distributional determinant for deformations with finite energy
- Variational Analysis in Sobolev andBVSpaces
- Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings
- Global invertibility of Sobolev functions and the interpenetration of matter
- Weakly Differentiable Functions
- Change of variables formula under minimal assumptions
- 3D-2D Asymptotic Analysis for Micromagnetic Thin Films
- Frank energy for nematic elastomers: a nonlinear model
- Existence of Energy Minimizers for Magnetostrictive Materials
- The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity
- Semicontinuity problems in the calculus of variations
- Direct methods in the calculus of variations
- On the existence of minimizers with prescribed singular points in nonlinear elasticity
This page was built for publication: Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers
