Anisotropic energies for the modeling of cavitation in nonlinear elasticity
Abstract
We study free-discontinuity functionals in nonlinear elasticity, where discontinuities correspond to the phenomenon of cavitation. The energy comprises two terms: a volume term accounting for the elastic energy, and a surface term concentrated on the boundaries of the cavities in the deformed configuration that depends on their unit normal. First, we prove the existence of energy-minimizing deformations. While the treatment of the volume term is standard, that of the surface term relies on the regularity of inverse deformations, their weak continuity properties, and Ambrosio’s lower semicontinuity theorem for special functions of bounded variation. Additionally, we identify sufficient conditions for minimality by employing outer variations and applying the formula for the first derivative of the anisotropic perimeter.
Acknowledgements
The author acknowledges the support of the Alexander von Humboldt Foundation through the Humboldt Research Fellowship. He is member of GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilitá e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica).
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© 2026 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On the second eigenvalue of the infinity Laplacian with Robin boundary conditions
- Smooth approximations for constant-mean-curvature hypersurfaces with isolated singularities
- The infinity-potential in the square
- A simple proof of the 1-dimensional flat chain conjecture
- Anisotropic energies for the modeling of cavitation in nonlinear elasticity
- On the Plateau problem for surfaces with minimum moment of inertia
- Existence theory for linear-growth variational integrals with signed measure data
Artikel in diesem Heft
- Frontmatter
- On the second eigenvalue of the infinity Laplacian with Robin boundary conditions
- Smooth approximations for constant-mean-curvature hypersurfaces with isolated singularities
- The infinity-potential in the square
- A simple proof of the 1-dimensional flat chain conjecture
- Anisotropic energies for the modeling of cavitation in nonlinear elasticity
- On the Plateau problem for surfaces with minimum moment of inertia
- Existence theory for linear-growth variational integrals with signed measure data
