Some Variational Problem in Morphoelasticity
- Ulisse Stefanelli, Professor, Chair of Applied Mathematics and Modeling University of Vienna
KAUST
I will present some recent work in collaboration with Elisa Davoli (TU Wien) and Katerina Nik (University of Vienna) on a three-dimensional quasistatic morpholelastic model. The mechanical response of the body and its growth are modeled by the interplay of hyperelastic energy minimization and growth dynamics. An existence result is obtained by regularization and time-discretization, also taking advantage of an exponential-update scheme. Then, we allow the growth dynamics to depend on an additional scalar field describing a nutrient, and formulate an optimal control problem. Eventually, we tackle the existence of coupled morphoelastic and nutrient solutions, when the latter is allowed to diffuse and interact with the growing body. The preprint is available as arXiv:2110.05566.
Overview
Abstract
I will present some recent work in collaboration with Elisa Davoli (TU Wien) and Katerina Nik (University of Vienna) on a three-dimensional quasistatic morpholelastic model. The mechanical response of the body and its growth are modeled by the interplay of hyperelastic energy minimization and growth dynamics. An existence result is obtained by regularization and time-discretization, also taking advantage of an exponential-update scheme. Then, we allow the growth dynamics to depend on an additional scalar field describing a nutrient, and formulate an optimal control problem. Eventually, we tackle the existence of coupled morphoelastic and nutrient solutions, when the latter is allowed to diffuse and interact with the growing body. The preprint is available as arXiv:2110.05566.
Brief Biography
Ulisse Stefanelli is a Professor of Mathematics at the University of Vienna, Austria, within the Chair of Applied Mathematics and Modeling. His research interests include Partial Differential Equations, the Calculus of Variations and Continuum Thermomechanics.