Pressure live loads and the variational derivation of linear elasticity

DOI10.1017/prm.2022.79arXiv2203.04078MaRDI QIDQ6070319

Publication date: 20 November 2023

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.04078

zbMATH Keywords

nonlinear elasticity gamma-convergence live load pressure load strong minimizer convergence weakly coercive elastic energy density

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

Unnamed Item
From non linear elasticity to linear elasticity with initial stress via $\Gamma$-convergence
Derivation of a rod theory for biphase materials with dislocations at the interface
A derivation of linearized Griffith energies from nonlinear models
Linear elasticity obtained from finite elasticity by $\Gamma $-convergence under weak coerciveness conditions
Surface interaction potentials in elasticity
A variational justification of linear elasticity with residual stress
$\Gamma $-convergence for incompressible elastic plates
Linear $\Gamma $-limits of multiwell energies in nonlinear elasticity theory
A variational approach to live loadings in finite elasticity
An introduction to $\Gamma$-convergence
Linearized elasticity as $\Gamma$-limit of finite elasticity
Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals
Linearized plasticity is the evolutionary $\Gamma$-limit of finite plasticity
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
Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials
Linearization of elasticity models for incompressible materials
Variational linearization of pure traction problems in incompressible elasticity
Korn's second inequality and geometric rigidity with mixed growth conditions
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
From finite to linear elastic fracture mechanics by scaling
Sets of Finite Perimeter and Geometric Variational Problems
Line-Tension Model for Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy
On the Passage from Nonlinear to Linearized Viscoelasticity
A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
From atomistic systems to linearized continuum models for elastic materials with voids
Geometric linearization of theories for incompressible elastic materials and applications
From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions
Mathematical Methods in Continuum Mechanics of Solids
Scaling in fracture mechanics by Bažant law: From finite to linearized elasticity

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