Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals

DOI10.1007/s00205-018-1240-6zbMath1398.35229OpenAlexW2791971464MaRDI QIDQ1783944

Mariapia Palombaro, Giuliano Lazzaroni, Gianni Dal Maso, Roberto Alicandro

Publication date: 21 September 2018

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: http://sro.sussex.ac.uk/id/eprint/74301/1/__smbhome.uscs.susx.ac.uk_bw233_Desktop_SRO_SRO%20-%20Maria%20Palombaro_ADMLP_linear_v3.pdf

zbMATH Keywords

singular perturbationGamma-convergencelinearised elasticity

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Linear elasticity with initial stresses (74B10) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (11)

Linearization of elasticity models for incompressible materials ⋮ Pressure live loads and the variational derivation of linear elasticity ⋮ Variational linearization of pure traction problems in incompressible elasticity ⋮ Microscopic Validation of a Variational Model of Epitaxially Strained Crystalline Films ⋮ Geometric linearization of theories for incompressible elastic materials and applications ⋮ Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions ⋮ Sharp conditions for the linearization of finite elasticity ⋮ Derivation of Linear Elasticity for a General Class of Atomistic Energies ⋮ The gap between linear elasticity and the variational limit of finite elasticity in pure traction problems ⋮ Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials ⋮ Nonlinear and linearized models in thermoviscoelasticity

Cites Work

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• On the effect of interactions beyond nearest neighbours on non-convex lattice systems
• Linear elasticity obtained from finite elasticity by \(\Gamma \)-convergence under weak coerciveness conditions
• Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory
• An introduction to \(\Gamma\)-convergence
• Linearized elasticity as \(\Gamma\)-limit of finite elasticity
• Rigidity estimate for two incompatible wells
• Microstructures with finite surface energy: The two-well problem
• On the derivation of linear elasticity from atomistic models
• A derivation of linear elastic energies from pair-interaction atomistic systems
• Simple proof of two-well rigidity
• Weakly Differentiable Functions
• A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
• 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
• Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance

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