Browsing by Author "Rausch, Manuel K."

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    Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations
    (2023) Taç, Vahidullah; Rausch, Manuel K.; Sahli Costabal, Francisco; Tepole, Adrian Buganza
    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.
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    Generative hyperelasticity with physics-informed probabilistic diffusion fields
    (2024) Tac, Vahidullah; Rausch, Manuel K.; Bilionis, Ilias; Sahli Costabal, Francisco; Tepole, Adrian Buganza
    Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that-by construction-create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticity.