1. On automated model discovery and a universal material subroutine for hyperelastic materials
- Author
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Peirlinck, M. (author), Linka, Kevin (author), Hurtado, Juan A. (author), Kuhl, Ellen (author), Peirlinck, M. (author), Linka, Kevin (author), Hurtado, Juan A. (author), and Kuhl, Ellen (author)
- Abstract
Constitutive modeling is the cornerstone of computational and structural mechanics. In a finite element analysis, the constitutive model is encoded in the material subroutine, a function that maps local strains onto stresses. This function is called within every finite element, at each integration point, within every time step, at each Newton iteration. Today's finite element packages offer large libraries of material models to choose from. However, the scientific criteria for appropriate model selection remain highly subjective and prone to user bias. Here we fully automate the process of model selection, autonomously discover the best model and parameters from experimental data, encode all possible discoverable models into a single material subroutine, and seamlessly integrate this universal material subroutine into a finite element analysis. We prototype this strategy for incompressible, isotropic, hyperelastic soft matter systems that we characterize through a combination of twelve possible terms. These terms feature the first and second invariants, raised to the first and second powers, embedded in the identity, exponential, and logarithmic functions, generating 22×2×3= 4096 models in total. We demonstrate how to integrate these models into a single universal material subroutine that features the classical neo Hooke, Blatz Ko, Mooney Rivlin, Demiray, Gent, and Holzapfel models as special cases. Finite element simulations with our new universal material subroutine show that it specializes well to these widely used models, generalizes well to newly discovered models, and agrees excellently with both experimental data and previous simulations. It also performs well within realistic finite element simulations and accurately predicts stress concentrations in the human brain for six different head impact scenarios. We anticipate that integrating automated model discovery into a universal material subroutine will generalize naturally to more complex comp, Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Medical Instruments & Bio-Inspired Technology
- Published
- 2024
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