Relaxation in \(BV\) versus quasiconvexification in \(W^{1,p}\); a model for the interaction between fracture and damage

DOI10.1007/BF01187895zbMath0847.73077OpenAlexW2037032846MaRDI QIDQ1902315

Gilles A. Francfort, Irene Fonseca

Publication date: 13 October 1996

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01187895

zbMATH Keywords

configurational forcesglobal stabilitypotential energycrack propagationyield criterionquasistatic evolutiondeformation fieldbrittle elastic continuumchoice of solution

Mathematics Subject Classification ID

Related Items (17)

Unnamed Item ⋮ Homogenization of free discontinuity problems ⋮ REGULAR APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS ⋮ Relaxation of variational problems under trace constraints ⋮ ANALYSIS OF OPTICAL FLOW MODELS IN THE FRAMEWORK OF THE CALCULUS OF VARIATIONS ⋮ Existence of minimizers for non-quasiconvex functionals arising in optimal design ⋮ Variational homogenization: old and new ⋮ A change of variables formula for mappings in BV ⋮ Regularity results for equilibria in a variational model for fracture ⋮ Rate-independent evolution of sets ⋮ Unnamed Item ⋮ Quasistatic evolution of a brittle thin film ⋮ A quasistatic evolution model for the interaction between fracture and damage ⋮ A variational approach to the local character of \(G\)-closure: the convex case ⋮ From adhesive to brittle delamination in visco-elastodynamics ⋮ Relaxation of bulk and interfacial energies ⋮ Existence of minimizers for a class of anisotropic free discontinuity problems

Cites Work

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• Relaxation of quasiconvex functionals in \(BV(\Omega, \mathbb{R}^ N)\) for integrands \(f(x, u, \bigtriangledown u)\)
• \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
• Variational problems in SBV and image segmentation
• Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals
• Homogenization of nonconvex integral functionals and cellular elastic materials
• Functionals with linear growth defined on vector valued BV functions
• The relaxation of a double-well energy
• On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals
• Periodic solutions and homogenization of non linear variational problems
• A new proof of the SBV compactness theorem
• Relaxation of bulk and interfacial energies
• Further remarks on the lower semicontinuity of polyconvex integrals
• The lower quasiconvex envelope of the stored energy function for an elastic crystal
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Weakly Differentiable Functions
• Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
• Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials
• On the lower semicontinuity of quasiconvex integrals in SBV(Ω, Rk)
• A General Chain Rule for Distributional Derivatives
• Semicontinuity problems in the calculus of variations
• Direct methods in the calculus of variations

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