Existence of minimizers for the \(2d\) stationary Griffith fracture model
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Publication:338051
DOI10.1016/j.crma.2016.09.003zbMath1351.49012arXiv1603.02843OpenAlexW2964105306MaRDI QIDQ338051
Matteo Focardi, Sergio Conti, Flaviana Iurlano
Publication date: 3 November 2016
Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.02843
Brittle fracture (74R10) Methods involving semicontinuity and convergence; relaxation (49J45) Theoretical approximation in context of PDEs (35A35) Brittle damage (74R05)
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Cites Work
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- Existence of minimizers for the \(2d\) stationary Griffith fracture model
- On the structure of \({\mathcal A}\)-free measures and applications
- Density lower bound estimates for local minimizers of the \(2d\) Mumford-Shah energy
- Generalised functions of bounded deformation
- A density result for GSBD and its application to the approximation of brittle fracture energies
- Dual spaces of stresses and strains, with applications to Hencky plasticity
- Piecewise rigidity
- Compactness and lower semicontinuity properties in \(SBD(\Omega)\)
- Existence of the displacements field for an elasto-plastic body subject to Hecky's law and von Mises yield condition
- Functions of bounded deformation
- Fine properties of functions with bounded deformation
- Singular sets of minimizers for the Mumford-Shah functional
- Existence theorem for a minimum problem with free discontinuity set
- An approximation result for special functions with bounded deformation
- Revisiting brittle fracture as an energy minimization problem
- Korn-Poincare inequalities for functions with a small jump set
- An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
- Optimal approximations by piecewise smooth functions and associated variational problems
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- The Variational Approach to Fracture
- Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance
