Growth is a fundamental process in biological systems and various technological applications, including epitaxial deposition and additive manufacturing. The interaction between growth and mechanics in deformable bodies leads to a wealth of very challenging mathematical questions. I will give a short overview of the key concepts of morphoelasticity, namely, the theory of elastic deformations in growing bodies. Unlike the classical case, the reference state of a growing body evolves over time, also in response to external stimuli and stress. I will discuss the case of surface accretion, which presents specific challenges. The emphasis will be on developing a variational framework where the existence of quasistatic morphoelastic evolution can be proved.
This talk is based on a collaboration with Elisa Davoli (TU Wien), Ulisse Stefanelli (University of Vienna), and Giuseppe Tomassetti (Roma Tre University).
