An existence result for accretive growth in elastic solids

Author:

Davoli Elisa1ORCID,Nik Katerina2,Stefanelli Ulisse234ORCID,Tomassetti Giuseppe5ORCID

Affiliation:

1. Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria

2. University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria

3. University of Vienna, Vienna Research Platform on Accelerating Photoreaction Discovery, Währingerstraße 17, 1090 Wien, Austria

4. Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, I-27100 Pavia, Italy

5. Dipartimento di Ingegneria, Università degli Studi Roma Tre, via Volterra 62, I-00146 Roma, Italy

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.

Funder

Austrian Science Fund

BMBWF through the OeAD-WTZ

Publisher

World Scientific Pub Co Pte Ltd

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