An existence result for accretive growth in elastic solids

Elisa Davoli, Katerina Nik, Ulisse Stefanelli, Giuseppe Tomassetti

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

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.

OriginalspracheEnglisch
Seiten (von - bis)2169-2190
Seitenumfang22
FachzeitschriftMathematical Models and Methods in Applied Sciences
Jahrgang34
Ausgabenummer11
DOIs
PublikationsstatusVeröffentlicht - 1 Okt. 2024

ÖFOS 2012

  • 101002 Analysis

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