Abstract
The small-deformation limit of finite elasticity is considered in presence of a given crack. The rescaled finite energies with the constraint of global injectivity are shown to Γ-converge to the linearized elastic energy with a local constraint of non-interpenetration along the crack.
Funding statement: The research was partially supported by Deutsche Forschungsgemeinschaft (DFG) via MATHEON project C18 (Analysis and Numerics of Multidimensional Models for Elastic Phase Transformations in Shape Memory Alloys) and via the project C05 (Effective Models for Interfaces with Many Scales) in the collaborative research center SFB 1114 Scaling Cascades in Complex Systems.
Acknowledgements
We thank the unknown referee for a very careful reading, which helped us to improve and correct some of our arguments.
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Articles in the same Issue
- Frontmatter
- On the regularity of solutions to the plastoelasticity problem
- Symmetry and asymmetry of minimizers of a class of noncoercive functionals
- Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks
- Finite energy solutions to inhomogeneous nonlinear elliptic equations with sub-natural growth terms
- Conical square functions for degenerate elliptic operators
Articles in the same Issue
- Frontmatter
- On the regularity of solutions to the plastoelasticity problem
- Symmetry and asymmetry of minimizers of a class of noncoercive functionals
- Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks
- Finite energy solutions to inhomogeneous nonlinear elliptic equations with sub-natural growth terms
- Conical square functions for degenerate elliptic operators