Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations

TL;DR

This paper introduces a neural ODE-based data-driven model for anisotropic finite viscoelasticity that respects physical laws and can handle complex, large deformation behaviors in various materials.

Contribution

It develops a novel neural ODE framework replacing traditional energy and dissipation functions with data-driven counterparts that satisfy thermodynamic constraints.

Findings

Model accurately predicts viscoelastic behavior of biological and synthetic materials.

Outperforms traditional viscoelastic models in various tests.

Handles large deformations and arbitrary loads in three dimensions.

Abstract

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.