Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations

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.

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• Deep Learning in Deterministic Computational Mechanics
• Theory and implementation of inelastic Constitutive Artificial Neural Networks
• A comparative study on different neural network architectures to model inelasticity
• Data-adaptive spline surfaces for non-separable hyperelastic energy functions
• A physics-augmented neural network framework for finite strain incompressible viscoelasticity