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

TL;DR

This paper introduces a new macroscopic model for stress-driven anisotropic growth in soft tissues, utilizing a growth potential concept and visco-plasticity methods to better capture complex biological growth behaviors.

Contribution

It proposes a novel approach that replaces predefined growth tensors with a general growth potential, enabling flexible modeling of isotropic and anisotropic tissue growth.

Findings

Model can simulate both isotropic and anisotropic growth.

Framework adapts to changing boundary and loading conditions.

Comparison shows advantages over standard isotropic growth models.

Abstract

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.