Integral representation for energies in linear elasticity with surface discontinuities
From MaRDI portal
Publication:2086111
DOI10.1515/acv-2020-0047zbMath1504.31013arXiv2005.06866OpenAlexW3100533495MaRDI QIDQ2086111
Francesco Solombrino, Vito Crismale, Manuel Friedrich
Publication date: 20 October 2022
Published in: Advances in Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.06866
Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Integral representations, integral operators, integral equations methods in two dimensions (31A10)
Related Items (3)
From atomistic systems to linearized continuum models for elastic materials with voids ⋮ On some non-local approximation of nonisotropic Griffith-type functionals ⋮ Integral representation and \(\Gamma\)-convergence for free-discontinuity problems with \(p(\cdot)\)-growth
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the structure of \({\mathcal A}\)-free measures and applications
- Generalised functions of bounded deformation
- Integral representation for functionals defined on \(SBD^p\) in dimension two
- Homogenization of the Neumann problem in perforated domains: an alternative approach
- Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures
- Functionals defined on partitions in sets of finite perimeter. I: Integral representation and Gamma-convergence
- Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization
- Compactness and lower semicontinuity properties in \(SBD(\Omega)\)
- Integral representation on \(BV(\Omega )\) of \(\Gamma\)-limits of variational integrals
- \(\Gamma\)-limits of integral functionals
- Some properties of Gamma-limits of integral functionals
- A global method for relaxation
- Integral representation of local functionals
- Integral representation results for functionals defined on \(\text{SBV}(\Omega;\mathbb{R}^ m)\)
- Fine properties of functions with bounded deformation
- A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
- A density result in \(GSBD^p\) with applications to the approximation of brittle fracture energies
- 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
- Functionals defined on piecewise rigid functions: integral representation and \(\Gamma \)-convergence
- Korn and Poincaré-Korn inequalities for functions with a small jump set
- Quantitative analysis of finite-difference approximations of free-discontinuity problems
- Phase-field approximation for a class of cohesive fracture energies with an activation threshold
- Homogenization of free discontinuity problems
- A compactness result in \(GSBV^p\) and applications to \(\varGamma \)-convergence for free discontinuity problems
- \(\Gamma\)-convergence of free-discontinuity problems
- Quasi-convexity and the lower semicontinuity of multiple integrals
- A Bridging Mechanism in the Homogenization of Brittle Composites with Soft Inclusions
- Integral representation and relaxation of local functionals
- FRACTURE MECHANICS IN PERFORATED DOMAINS: A VARIATIONAL MODEL FOR BRITTLE POROUS MEDIA
- 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?
- On the Integral Representation of Variational Functionals on $BD$
- VI. The phenomena of rupture and flow in solids
- A characterization of nonlinear functionals on Sobolev spaces which admit an integral representation with a Carathéodory integrand
This page was built for publication: Integral representation for energies in linear elasticity with surface discontinuities
