Macroscopic modelling of stress driven anisotropic growth in bioengineered tissues

• Published in: Proceedings in applied mathematics and mechanics Vol. 21; no. 1
• Main Authors: Lamm, Lukas, Holthusen, Hagen, Böhm, Christian, Jockenhövel, Stefan, Reese, Stefanie
• Format: Journal Article
• Language: English
• Published: Berlin Wiley-VCH GmbH 01.12.2021
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.202100046

Within this contribution we present a new approach to macroscopically describe stress‐driven volumetric growth occurring in soft tissues. To overcome the limitations of an a‐priori prescribed structure of the growth tensor, the existence of a general growth potential is postulated. Such a potential aims to describe a homeostatic stress state that is ultimately reached as a result of the growth process. Similar to well established methods from the field of visco‐plasticity, we formulate the evolution of the growth related right Cauchy‐Green tensor as a time dependent associative evolution law with respect to the given growth potential. This approach is not restricted to describe either isotropic or anisotropic growth related changes in geometry, but can cover both, which gives the model a flexibility that many other established models are lacking. Besides the main aspects of the theoretical development, we also show numerical examples comparing the newly derived model with a standard formulation of isotropic growth.