Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations. (English) Zbl 1539.74005
Summary: 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.
MSC:
| 74-10 | Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids |
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 74B20 | Nonlinear elasticity |
Keywords:
viscoelasticity; neural ordinary differential equations; data-driven mechanics; tissue mechanics; nonlinear mechanics; physics-informed machine learningReferences:
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