On the Approximation of SBD Functions and Some Applications
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Publication:5205887
DOI10.1137/18M119522XzbMath1429.26023arXiv1806.03076OpenAlexW4319655217MaRDI QIDQ5205887
Publication date: 17 December 2019
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.03076
strong approximation\(\Gamma\)-convergencefree discontinuity problemscohesive fracturespecial functions of bounded deformation
Fracture and damage (74R99) Variational problems in a geometric measure-theoretic setting (49Q20) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) PDEs in connection with mechanics of deformable solids (35Q74)
Related Items (10)
Korn and Poincaré-Korn inequalities for functions with a small jump set ⋮ Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity ⋮ Lower semicontinuity for functionals defined on piecewise rigid functions and on \(GSBD\) ⋮ A density result in \(GSBD^p\) with applications to the approximation of brittle fracture energies ⋮ Phase-field approximation for a class of cohesive fracture energies with an activation threshold ⋮ Phase-field approximation of functionals defined on piecewise-rigid maps ⋮ Existence of strong solutions to the Dirichlet problem for the Griffith energy ⋮ Damage-driven fracture with low-order potentials: asymptotic behavior, existence and applications ⋮ Density in SBD and approximation of fracture energies ⋮ Lower semicontinuity inGSBDfor nonautonomous surface integrals
Cites Work
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- Phase field approximation of cohesive fracture models
- Generalised functions of bounded deformation
- A density result for GSBD and its application to the approximation of brittle fracture energies
- Integral representation for functionals defined on \(SBD^p\) in dimension two
- A derivation of linearized Griffith energies from nonlinear models
- A new approximation result for BV-functions
- A nonlocal approximation of free discontinuity problems in SBV and SBD
- Existence theory for a new class of variational problems
- Compactness and lower semicontinuity properties in \(SBD(\Omega)\)
- On the existence of the fields of stresses and displacements for an elasto-perfectly plastic body in static equilibrium
- New integral estimates for deformations in terms of their nonlinear strains
- Integral representation results for functionals defined on \(\text{SBV}(\Omega;\mathbb{R}^ m)\)
- Fine properties of functions with bounded deformation
- A finite element approximation of the Griffith's model in fracture mechanics
- Quasistatic crack growth in 2d-linearized elasticity
- Existence of strong minimizers for the Griffith static fracture model in dimension two
- A density result in \(GSBD^p\) with applications to the approximation of brittle fracture energies
- Approximation of a brittle fracture energy with a constraint of non-interpenetration
- An approximation result for special functions with bounded deformation
- Phase-field approximation for a class of cohesive fracture energies with an activation threshold
- Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy
- Density in SBD and approximation of fracture energies
- On the approximation of SBV functions
- Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case
- A Bridging Mechanism in the Homogenization of Brittle Composites with Soft Inclusions
- Korn-Poincare inequalities for functions with a small jump set
- Asymptotic Analysis of Ambrosio--Tortorelli Energies in Linearized Elasticity
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- Traces of functions of bounded deformation
- On Korn's second inequality
- A Piecewise Korn Inequality in SBD and Applications to Embedding and Density Results
- A Korn-type inequality in SBD for functions with small jump sets
- Which special functions of bounded deformation have bounded variation?
- A density result in SBV with respect to non-isotropic energies
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