Predicting the Mechanical Properties of Biopolymer Gels Using Neural Networks Trained on Discrete Fiber Network Data

TL;DR

This paper develops a neural network model trained on fiber network data to predict the macroscale mechanical behavior of biopolymer gels efficiently, bridging microscale structure and macroscale mechanics.

Contribution

The authors introduce a fully connected neural network trained on fiber network simulations to accurately and efficiently model biopolymer gel mechanics at the macroscale.

Findings

Neural network accurately predicts fiber network behavior.

Model integrated into Abaqus for finite element simulations.

Enables multiscale modeling of biological materials.

Abstract

Biopolymer gels, such as those made out of fibrin or collagen, are widely used in tissue engineering applications and biomedical research. Moreover, fibrin naturally assembles into gels in vivo during wound healing and thrombus formation. Macroscale biopolymer gel mechanics are dictated by the microscale fiber network. Hence, accurate description of biopolymer gels can be achieved using representative volume elements (RVE) that explicitly model the discrete fiber networks of the microscale. These RVE models, however, cannot be efficiently used to model the macroscale due to the challenges and computational demands of multiscale coupling. Here, we propose the use of an artificial, fully connected neural network (FCNN) to efficiently capture the behavior of the RVE models. The FCNN was trained on 1100 fiber networks subjected to 121 biaxial deformations. The stress data from the RVE, together with the total energy and the condition of incompressibility of the surrounding matrix, were used to determine the derivatives of an unknown strain energy function with respect to the deformation invariants. During training, the loss function was modified to ensure convexity of the strain energy function and symmetry of its Hessian. A general FCNN model was coded into a user material subroutine (UMAT) in the software Abaqus. In this work, the FCNN trained on the discrete fiber network data was used in finite element simulations of fibrin gels using our UMAT. We anticipate that this work will enable further integration of machine learning tools with computational mechanics. It will also improve computational modeling of biological materials characterized by a multiscale structure.