Abstract
We investigate a model for the accretive growth of an elastic solid. The reference configuration of the body is accreted in its normal direction, with space- and deformation-dependent accretion rate. The time-dependent reference configuration is identified via the level sets of the unique viscosity solution of a suitable generalized eikonal equation. After proving the global-in-time well-posedness of the quasistatic equilibrium under prescribed growth, we prove the existence of a local-in-time solution for the coupled equilibrium-growth problem, where both mechanical displacement and time-evolving set are unknown. A distinctive challenge is the limited regularity of the growing body, which calls for proving a new uniform Korn inequality.
Originalsprache | Englisch |
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Seiten (von - bis) | 2169-2190 |
Seitenumfang | 22 |
Fachzeitschrift | Mathematical Models and Methods in Applied Sciences |
Jahrgang | 34 |
Ausgabenummer | 11 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Okt. 2024 |
ÖFOS 2012
- 101002 Analysis