Calculus of Variations and Geometric Measure Theory

E. Davoli - K. Nik - U. Stefanelli - G. Tomassetti

An existence result for accretive growth in elastic solids

created by davoli on 13 Mar 2024


Submitted Paper

Inserted: 13 mar 2024
Last Updated: 13 mar 2024

Year: 2024


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: existence, viscosity solution, quasistatic evolution, Accretive growth, Elastic solids, Variational formulation