Viscoelasticity Neural Ordinary Differential Equations Data-driven Mechanics Tissue Mechanics Nonlinear Mechanics Physics-informed Machine Learning

External authors:

• Vahidullah Tac ( Purdue University )
• Manuel K. Rausch ( University of Texas Austin )
• Adrian Buganza Tepole ( Purdue University West Lafayette Campus , Purdue University )

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 human brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.(c) 2023 Elsevier B.V. All rights reserved.