Calculus of Variations and Geometric Measure Theory

E. Davoli - K. Nik - U. Stefanelli

Existence results for a morphoelastic model

created by davoli on 11 Oct 2021
modified on 19 Apr 2022


Accepted Paper

Inserted: 11 oct 2021
Last Updated: 19 apr 2022

Journal: ZAMM- Zeitschrift für Angewandte Mathematik und Mechanik
Year: 2021


We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor and is ruled by the interplay of hyperelastic energy minimization and growth dynamics. By introducing a regularization in the model, we prove that solutions can be obtained as limits of time-discrete solutions, built by means of an exponential-update scheme. By further allowing the dependence of growth dynamics on an additional scalar field, to be interpreted as a nutrient or inhibitor, we formulate an optimal control problem and prove existence of optimal controls and states. Eventually, we tackle the existence of coupled morphoelastic and nutrient solutions, when the latter is allowed to diffuse and interact with the growing body.

Keywords: existence, optimal control, Morphoelasticity, nutrient dynamics