Efficient time-stepping for the evolution equations of damage-induced growth and remodelling in soft biological tissues

authored by: Igor Tagiltsev, Peter Wriggers
Abstract: The constrained mixture method is a powerful instrument to model soft biological tissues, in particular — their growth and remodelling (G&R) behaviour. Its clear drawback lays in the increase of governing equations which corresponds to the increase of material constituents. In the current paper we scrutinise a particular G&R model, that is based on the detailed description of material's chemo-mechano-biological state, caused by excessive load associated with collagen fibres’ unfolding. The model consist of many interacting evolution equations, solving of which takes most of computational time during applied simulations. Two qualitative model assumptions are made to improve its capabilities. Moreover, several iteration-free numerical schemes are introduced addressing the integration of evolution equations. We show that the numerical performance of the model drastically improves with the proposed schemes, while no compromises with respect to robustness or accuracy of the simulation are made.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: European Journal of Mechanics, A/Solids
Volume: 111
No. of pages: 9
ISSN: 0997-7538
Publication date: 21.01.2025
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: General Materials Science, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy
Electronic version(s): https://doi.org/10.1016/j.euromechsol.2025.105582 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{cb43c422f9674881b8f57b4213cbe58c,
title = "Efficient time-stepping for the evolution equations of damage-induced growth and remodelling in soft biological tissues",
abstract = "The constrained mixture method is a powerful instrument to model soft biological tissues, in particular — their growth and remodelling (G&R) behaviour. Its clear drawback lays in the increase of governing equations which corresponds to the increase of material constituents. In the current paper we scrutinise a particular G&R model, that is based on the detailed description of material's chemo-mechano-biological state, caused by excessive load associated with collagen fibres{\textquoteright} unfolding. The model consist of many interacting evolution equations, solving of which takes most of computational time during applied simulations. Two qualitative model assumptions are made to improve its capabilities. Moreover, several iteration-free numerical schemes are introduced addressing the integration of evolution equations. We show that the numerical performance of the model drastically improves with the proposed schemes, while no compromises with respect to robustness or accuracy of the simulation are made.",
keywords = "Damage-induced growth, Efficient numerics, Soft biological tissue",
author = "Igor Tagiltsev and Peter Wriggers",
note = "Publisher Copyright: {\textcopyright} 2025 The Author(s)",
year = "2025",
month = jan,
day = "21",
doi = "10.1016/j.euromechsol.2025.105582",
language = "English",
volume = "111",
journal = "European Journal of Mechanics, A/Solids",
issn = "0997-7538",
publisher = "Elsevier BV",
}