セミナーの予定

2024年10月3日(木) 16:30-18:00

会場

東北大学 合同A棟8階801室

発表者

Ulisse Stefanelli 氏 (University of Vienna)

題目

Free-boundary problems for accretive growth

要旨

Accretive growth is a fundamental process in biological systems, as well as in various technological contexts, including epitaxial deposition and additive manufacturing. The interaction between growth and mechanics in deformable bodies gives rise to a wealth of very challenging mathematical questions. I will provide a brief overview of the fundamental concepts of morphoelasticity, namely, the theory of elastic deformations in growing bodies. In contrast to the classical case, the reference state of a growing body evolves over time, also in response to external stimuli and stress. In some situations, this calls for free-boundary formulations, as the actual shape of the undeformed body is also unknown. I plan to discuss the case of surface accretion, which poses specific challenges. The focus will be the development of a variational framework where the existence of three-dimensional morphoelastic evolution can be proved, both in the infinitesimal and in the finite deformation case. This is work in collaboration with Andrea Chiesa (University of Vienna), Elisa Davoli (TU Vienna), Katerina Nik (TU Delft), and Giuseppe Tomassetti (Roma 3).