# A macroscopic approach for stress driven anisotropic growth in bioengineered soft tissues

arXiv: https://arxiv.org/abs/2107.03698 · HTML: https://mlsanity.com/paper/2107.03698/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2021.

## Built on by (most cited first, 3 of 3)

- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2407.19326/) (2024)
- [Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling](https://mlsanity.com/paper/2410.13645/) (2024)

## Abstract (arXiv)

The simulation of growth processes within soft biological tissues is of utmost importance for many applications in the medical sector. Within this contribution we propose a new macroscopic approach fro modelling stress-driven volumetric growth occurring in soft tissues. Instead of using the standard approach of a-priori defining the structure of the growth tensor, we postulate the existance of a general growth potential. Such a potential describes all eligable homeostatic stress states that can ultimately be reached as a result of the growth process. Making use of well established methods from visco-plasticity, the evolution of the growth related right Cauchy-Green tensor is subsequently defined as a time dependent associative evolution law with respect to the introduced potential. This approach naturally leads to a formulation that is able to cover both, isotropic and anisotropic growth related changes in geometry. It furthermore allows the model to flexibly adapt to changing boundary and loading conditions. Besides the theoretical development, we also describe the algorithmic implementation and furthermore compare the newly derived model with a standard formulation of isotropic growth.