Qualitative properties of a continuum theory for thin films

DOI10.1016/j.anihpc.2006.09.001zbMath1142.74026OpenAlexW1963909781MaRDI QIDQ2475784

Bernd Schmidt

Publication date: 11 March 2008

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/78783

zbMATH Keywords

discrete-to-continuum limits

Mathematics Subject Classification ID

Thin films (74K35) Molecular, statistical, and kinetic theories in solid mechanics (74A25)

Related Items (4)

An atomistic derivation of von-Kármán plate theory ⋮ A continuum model for brittle nanowires derived from an atomistic description by \(\Gamma \)-convergence ⋮ On the passage from atomic to continuum theory for thin films ⋮ Multi-value microstructural descriptors for complex materials: analysis of ground states

Cites Work

• Convexity conditions and existence theorems in nonlinear elasticity
• An introduction to \(\Gamma\)-convergence
• Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
• Rigorous derivation of nonlinear plate theory and geometric rigidity
• Variational methods for crystalline microstructure. Analysis and computation
• From molecular models to continuum mechanics
• The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus
• NON-LOCAL VARIATIONAL LIMITS OF DISCRETE SYSTEMS
• Continuum Limits of Discrete Systems without Convexity Hypotheses
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Direct methods in the calculus of variations
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