A Physics-Informed Neural Network Framework for Simulating Creep Buckling in Growing Viscoelastic Biological Tissues

TL;DR

This paper introduces an energy-based physics-informed neural network framework that models viscoelastic creep, buckling, and growth in biological tissues, effectively capturing instabilities and morphological changes without traditional meshing or perturbations.

Contribution

It presents a novel PINN approach that implicitly enforces physical laws through energy minimization, enabling natural simulation of complex viscoelastic and growth-induced phenomena.

Findings

Successfully predicts creep buckling without pre-imposed imperfections

Captures post-buckling evolution and tissue morphology changes

Extends to biological growth and morphogenesis modeling

Abstract

Modeling viscoelastic behavior is crucial in engineering and biomechanics, where materials undergo time-dependent deformations, including stress relaxation, creep buckling and biological tissue development. Traditional numerical methods, like the finite element method, often require explicit meshing, artificial perturbations or embedding customised programs to capture these phenomena, adding computational complexity. In this study, we develop an energy-based physics-informed neural network (PINN) framework using an incremental approach to model viscoelastic creep, stress relaxation, buckling, and growth-induced morphogenesis. Physics consistency is ensured by training neural networks to minimize the systems potential energy functional, implicitly satisfying equilibrium and constitutive laws. We demonstrate that this framework can naturally capture creep buckling without pre-imposed imperfections, leveraging inherent training dynamics to trigger instabilities. Furthermore, we extend our framework to biological tissue growth and morphogenesis, predicting both uniform expansion and differential growth-induced buckling in cylindrical structures. Results show that the energy-based PINN effectively predicts viscoelastic instabilities, post-buckling evolution and tissue morphological evolution, offering a promising alternative to traditional methods. This study demonstrates that PINN can be a flexible robust tool for modeling complex, time-dependent material behavior, opening possible applications in structural engineering, soft materials, and tissue development.