Existence results for a morphoelastic model

Abstract: I will report on a 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 an interplay of hyperelastic energy minimization and growth dynamics. A first existence result is obtained by regularization and time-discretization, also taking advantage of an exponential-update scheme. We then allow the growth dynamics to depend on an additional scalar field, say 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.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).