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arXiv · 2403.08307

An existence result for accretive growth in elastic solids

Elisa Davoli·Katerina Nik·Ulisse Stefanelli·Giuseppe Tomassetti
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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.

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Elisa Davoli, Katerina Nik, Ulisse Stefanelli, Giuseppe Tomassetti. 2024-03-13. An existence result for accretive growth in elastic solids. https://arxiv.org/abs/2403.08307

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