Optimal flux densities for linear mappings and the multiscale geometry of structured deformations

DOI10.1007/s00205-015-0890-xzbMath1330.49049OpenAlexW377204975MaRDI QIDQ887924

Roberto Paroni, David R. Owen

Publication date: 4 November 2015

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

Full work available at URL: https://doi.org/10.1007/s00205-015-0890-x

zbMATH Keywords

relaxationintegral representation formulamultiscale geometryoptimal flux densitiesstructured deformation

Mathematics Subject Classification ID

Micromechanics of solids (74M25) Energy minimization in equilibrium problems in solid mechanics (74G65) Optimization of other properties in solid mechanics (74P10) Variational problems in a geometric measure-theoretic setting (49Q20) Micromechanical theories (74A60) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99)

Related Items (8)

Explicit formulas for relaxed disarrangement densities arising from structured deformations ⋮ The general form of the relaxation of a purely interfacial energy for structured deformations ⋮ A non-local asymptotic theory for thin elastic plates ⋮ Second-order structured deformations: relaxation, integral representation and applications ⋮ Upscaling and spatial localization of non-local energies with applications to crystal plasticity ⋮ Elasticity with hierarchical disarrangements: a field theory that admits slips and separations at multiple submacroscopic levels ⋮ Dimension reduction in the context of structured deformations ⋮ The variational structure of classical plasticity

Cites Work

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• A survey on structured deformations
• A Lusin type theorem for gradients
• Structured deformations of continua
• Bulk and interfacial energy densities for structured deformations of continua
• Second-order structured deformations
• Relaxation of bulk and interfacial energies
• Integral-gradient formulae for structured deformations
• On the approximation theorem for structured deformations from \(BV(\Omega)\)
• Structured Deformations as Energy Minimizers in Models of Fracture and Hysteresis
• The Energy of a One-Dimensional Structured Deformation

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