On the Representation of Effective Energy Densities

DOI10.1051/cocv:2000120zbMath0967.49025OpenAlexW2098474636MaRDI QIDQ2701813

Christopher J. Larsen

Publication date: 5 March 2001

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/90581

zbMATH Keywords

quasiconvexityintegral representationrelaxationbulk and surface integrals

Mathematics Subject Classification ID

Optimization of other properties in solid mechanics (74P10) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items (8)

Second-order structured deformations: relaxation, integral representation and applications ⋮ Upscaling and spatial localization of non-local energies with applications to crystal plasticity ⋮ Discrete stochastic approximations of the Mumford-Shah functional ⋮ \(\Gamma\)-convergence of free-discontinuity problems ⋮ \Gamma-convergence for free-discontinuity problems in linear elasticity: homogenization and relaxation ⋮ Homogenization of the Neumann problem in perforated domains: an alternative approach ⋮ A \(\Gamma\)-convergence approach to stability of unilateral minimality properties in fracture mechanics and applications ⋮ FRACTURE MECHANICS IN PERFORATED DOMAINS: A VARIATIONAL MODEL FOR BRITTLE POROUS MEDIA

Cites Work

• Lower semicontinuity in spaces of weakly differentiable functions
• Structured deformations of continua
• Bulk and interfacial energy densities for structured deformations of continua
• Analysis of Concentration and Oscillation Effects Generated by Gradients
• Quasiconvexification in W^1,1 and Optimal Jump Microstructure in BV Relaxation
• Direct methods in the calculus of variations
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