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1. Democratizing biomedical simulation through automated model discovery and a universal material subroutine

   https://doi.org/10.1007/s00466-024-02515-y  

   Peirlinck, Mathias; Linka, Kevin; Hurtado, Juan A; Holzapfel, Gerhard A; Kuhl, Ellen (June 2025, Computational Mechanics)

   Abstract Personalized computational simulations have emerged as a vital tool to understand the biomechanical factors of a disease, predict disease progression, and design personalized intervention. Material modeling is critical for realistic biomedical simulations, and poor model selection can have life-threatening consequences for the patient. However, selecting the best model requires a profound domain knowledge and is limited to a few highly specialized experts in the field. Here we explore the feasibility of eliminating user involvement and automate the process of material modeling in finite element analyses. We leverage recent developments in constitutive neural networks, machine learning, and artificial intelligence to discover the best constitutive model from thousands of possible combinations of a few functional building blocks. We integrate all discoverable models into the finite element workflow by creating a universal material subroutine that contains more than 60,000 models, made up of 16 individual terms. We prototype this workflow using biaxial extension tests from healthy human arteries as input and stress and stretch profiles across the human aortic arch as output. Our results suggest that constitutive neural networks can robustly discover various flavors of arterial models from data, feed these models directly into a finite element simulation, and predict stress and strain profiles that compare favorably to the classical Holzapfel model. Replacing dozens of individual material subroutines by a single universal material subroutine—populated directly via automated model discovery—will make finite element simulations more user-friendly, more robust, and less vulnerable to human error. Democratizing finite element simulation by automating model selection could induce a paradigm shift in physics-based modeling, broaden access to simulation technologies, and empower individuals with varying levels of expertise and diverse backgrounds to actively participate in scientific discovery and push the boundaries of biomedical simulation. 

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2. AI-dente: an open machine learning based tool to interpret nano-indentation data of soft tissues and materials

   https://doi.org/10.1039/D3SM00402C  

   Giolando, Patrick; Kakaletsis, Sotirios; Zhang, Xuesong; Weickenmeier, Johannes; Castillo, Edward; Dortdivanlioglu, Berkin; Rausch, Manuel K. (October 2023, Soft Matter)

   Nano-indentation is a promising method to identify the constitutive parameters of soft materials, including soft tissues. Especially when materials are very small and heterogeneous, nano-indentation allows mechanical interrogation where traditional methods may fail. However, because nano-indentation does not yield a homogeneous deformation field, interpreting the resulting load–displacement curves is non-trivial and most investigators resort to simplified approaches based on the Hertzian solution. Unfortunately, for small samples and large indentation depths, these solutions are inaccurate. We set out to use machine learning to provide an alternative strategy. We first used the finite element method to create a large synthetic data set. We then used these data to train neural networks to inversely identify material parameters from load–displacement curves. To this end, we took two different approaches. First, we learned the indentation forward problem, which we then applied within an iterative framework to identify material parameters. Second, we learned the inverse problem of directly identifying material parameters. We show that both approaches are effective at identifying the parameters of the neo-Hookean and Gent models. Specifically, when applied to synthetic data, our approaches are accurate even for small sample sizes and at deep indentation. Additionally, our approaches are fast, especially compared to the inverse finite element approach. Finally, our approaches worked on unseen experimental data from thin mouse brain samples. Here, our approaches proved robust to experimental noise across over 1000 samples. By providing open access to our data and code, we hope to support others that conduct nano-indentation on soft materials. 

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3. Hyper-Viscoelastic 3D Response of Axons Subjected to Repeated Tensile Loads in Brain White Matter

   https://doi.org/10.1115/IMECE2022-97059  

   Agarwal, Mohit; Pelegri, Assimina A. (October 2022, American Society of Mechanical Engineers)

   Abstract A novel finite element method (FEM) is developed to study mechanical response of axons embedded in extra cellular matrix (ECM) when subjected to harmonic uniaxial stretch under purely non-affine kinematic boundary conditions. The proposed modeling approach combines hyper-elastic (such as Ogden model) and time/frequency domain viscoelastic constitutive models to evaluate the effect of parametrically varying oligodendrocyte-axon tethering under harmonic stretch at 50Hz. A hybrid hyper-viscoelastic material (HVE) model enabled the analysis of repeated uniaxial load on stress propagation and damage accumulation in white matter. In the proposed FEM, oligodendrocyte connections to axons are depicted via a spring-dashpot model. This tethering technique facilitates contact definition at various locations, parameterizes connection points and varies stiffness of connection hubs. Results from a home-grown FE submodel configuration of a single oligodendrocyte tethered to axons at various locations are presented. Root mean square deviation (RMSD) are computed between stress-strain plots to depict trends in mechanical response. Steady-state dynamic (SSD) simulations show stress relaxation in axons. Gradual axonal softening under repetitive loads is illustrated employing Prony series - HVE models. Representative von-Mises stress plots indicate that undulated axons experience bending stresses along their tortuous path, suggesting greater susceptibility to damage accumulation and fatigue failure due to repeated strains. 

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4. An Entropy Dynamics Approach for Deriving and Applying Fractal and Fractional Order Viscoelasticity to Elastomers

   https://doi.org/10.1115/1.4062389  

   Pahari, Basanta R.; Stanisauskis, Eugenia; Mashayekhi, Somayeh; Oates, William (August 2023, Journal of Applied Mechanics)

   Abstract Entropy dynamics is a Bayesian inference methodology that can be used to quantify time-dependent posterior probability densities that guide the development of complex material models using information theory. Here, we expand its application to non-Gaussian processes to evaluate how fractal structure can influence fractional hyperelasticity and viscoelasticity in elastomers. We investigate how kinematic constraints on fractal polymer network deformation influences the form of hyperelastic constitutive behavior and viscoelasticity in soft materials such as dielectric elastomers, which have applications in the development of adaptive structures. The modeling framework is validated on two dielectric elastomers, VHB 4910 and 4949, over a broad range of stretch rates. It is shown that local fractal time derivatives are equally effective at predicting viscoelasticity in these materials in comparison to nonlocal fractional time derivatives under constant stretch rates. We describe the origin of this accuracy that has implications for simulating large-scale problems such as finite element analysis given the differences in computational efficiency of nonlocal fractional derivatives versus local fractal derivatives. 

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5. Deep 3D Convolution Neural Network Methods for Brain White Matter Hybrid Computational Simulations

   https://doi.org/10.1115/IMECE2020-24664  

   Wu, Xuehai; Pelegri, Assimina A. (November 2020, International Mechanical Engineering Congress and Exposition, IMECE 2020)

   Material properties of brain white matter (BWM) show high anisotropy due to the complicated internal three-dimensional microstructure and variant interaction between heterogeneous brain-tissue (axon, myelin, and glia). From our previous study, finite element methods were used to merge micro-scale Representative Volume Elements (RVE) with orthotropic frequency domain viscoelasticity to an integral macro-scale BWM. Quantification of the micro-scale RVE with anisotropic frequency domain viscoelasticity is the core challenge in this study. The RVE behavior is expressed by a viscoelastic constitutive material model, in which the frequency-related viscoelastic properties are imparted as storage modulus and loss modulus for the composite comprised of axonal fibers and extracellular glia. Using finite elements to build RVEs with anisotropic frequency domain viscoelastic material properties is computationally very consuming and resource-draining. Additionally, it is very challenging to build every single RVE using finite elements since the architecture of each RVE is arbitrary in an infinite data set. The architecture information encoded in the voxelized location is employed as input data and is consequently incorporated into a deep 3D convolution neural network (CNN) model that cross-references the RVEs’ material properties (output data). The output data (RVEs’ material properties) is calculated in parallel using an in-house developed finite element method, which models RVE samples of axon-myelin-glia composites. This novel combination of the CNN-RVE method achieved a dramatic reduction in the computation time compared with directly using finite element methods currently present in the literature. 

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