An existence result for accretive growth in elastic solids
Analysis of PDEs
2024-03-14 v1
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.
Keywords
Cite
@article{arxiv.2403.08307,
title = {An existence result for accretive growth in elastic solids},
author = {Elisa Davoli and Katerina Nik and Ulisse Stefanelli and Giuseppe Tomassetti},
journal= {arXiv preprint arXiv:2403.08307},
year = {2024}
}