Linearized elasticity as \(\Gamma\)-limit of finite elasticity

DOI10.1023/A:1016577431636zbMath1009.74008OpenAlexW314858373MaRDI QIDQ1611760

R. Smith

Publication date: 28 August 2002

Published in: Set-Valued Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1016577431636

zbMATH Keywords

hyperelastic materialweak topologystrong topologyLipschitz domaingamma convergenceconvergence of minimizerslinearized elastic energiesrescaled nonlinear energies

Mathematics Subject Classification ID

Related Items (51)

Existence and linearization for the Souza-Auricchio model at finite strains ⋮ Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations ⋮ Linearization of elasticity models for incompressible materials ⋮ Γ-convergence: a tool to investigate physical phenomena across scales ⋮ A nonlinear Korn inequality based on the Green-Saint Venant strain tensor ⋮ Unnamed Item ⋮ From non linear elasticity to linear elasticity with initial stress via \(\Gamma\)-convergence ⋮ On the Passage from Nonlinear to Linearized Viscoelasticity ⋮ A variational model for dislocations at semi-coherent interfaces ⋮ Pressure live loads and the variational derivation of linear elasticity ⋮ An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem ⋮ Surface penalization of self-interpenetration in linear and nonlinear elasticity ⋮ Linearization for finite plasticity under dislocation-density tensor regularization ⋮ The tapering length of needles in martensite/martensite macrotwins ⋮ Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture ⋮ Rigorous derivation of a homogenized bending-torsion theory for inextensible rods from three-dimensional elasticity ⋮ One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams ⋮ Variational linearization of pure traction problems in incompressible elasticity ⋮ Linearization and computation for large-strain visco-elasticity ⋮ Derivation of a homogenized bending-torsion theory for rods with micro-heterogeneous prestrain ⋮ A model of controlled growth ⋮ Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity ⋮ Commutability of homogenization and linearization at identity in finite elasticity and applications ⋮ Uniqueness of equilibrium with sufficiently small strains in finite elasticity ⋮ Geometric linearization of theories for incompressible elastic materials and applications ⋮ A derivation of linearized Griffith energies from nonlinear models ⋮ Finite Plasticity in $P^\top\!P$. Part II: Quasi-Static Evolution and Linearization ⋮ From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions ⋮ A variational justification of linear elasticity with residual stress ⋮ Linear elasticity obtained from finite elasticity by \(\Gamma \)-convergence under weak coerciveness conditions ⋮ On the commutability of homogenization and linearization in finite elasticity ⋮ Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals ⋮ From finite to linear elastic fracture mechanics by scaling ⋮ Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks ⋮ An analytical mechanics approach to the first law of thermodynamics and construction of a variational hierarchy ⋮ 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 ⋮ Derivation of Linear Elasticity for a General Class of Atomistic Energies ⋮ Asymptotic expansions by \(\Gamma \)-convergence ⋮ Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory ⋮ Characterizations of symmetric polyconvexity ⋮ A new variational approach to linearization of traction problems in elasticity ⋮ QUASI-STATIC EVOLUTIONS IN LINEAR PERFECT PLASTICITY AS A VARIATIONAL LIMIT OF FINITE PLASTICITY: A ONE-DIMENSIONAL CASE ⋮ The gap between linear elasticity and the variational limit of finite elasticity in pure traction problems ⋮ Convex integration arising in the modelling of shape-memory alloys: some remarks on rigidity, flexibility and some numerical implementations ⋮ Linear models of a stiffened plate via \(\Gamma \)-convergence ⋮ Scaling in fracture mechanics by Bažant law: From finite to linearized elasticity ⋮ Variational Problems for Föppl--von Kármán Plates ⋮ Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials ⋮ Asymptotic behavior of constrained local minimizers in finite elasticity ⋮ Nonlinear and linearized models in thermoviscoelasticity

This page was built for publication: Linearized elasticity as \(\Gamma\)-limit of finite elasticity