Inelastic material formulations based on a co-rotated intermediate configuration—Application to bioengineered tissues

Holthusen, Hagen; Rothkranz, Christiane; Lamm, Lukas; Brepols, Tim; Reese, Stefanie

doi:10.1016/j.jmps.2022.105174

Cited by 22 publications

(7 citation statements)

References 124 publications

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“…The underlying idea is to generalize the Holzapfel Ogden model and design an orthotropic, perfectly incompressible constitutive neural network that takes the two isotropic invariants I 1 , I 2 and the six anisotropic invariants I 4f , I 4s , I 4n , I 8fs , I 8fn , I 8sn as input and approximates the free energy function as output. This network has two hidden layers: the first layer generates powers (•) and (•) 2 of the invariants, and the second layer applies the identity (•) and exponential (exp(•)) to these powers [29,44,66]. This results in 8 × 2 × 2 = 32 terms, 48 model parameters, and 32 2 = 4.294.967.296 possible models.…”

Section: Motivationmentioning

confidence: 99%

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Martonová,

Peirlinck,

Linka

et al. 2024

Preprint

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For more than half a century, scientists have developed mathematical models to understand the behavior of the human heart. Today, we have dozens of heart tissue models to choose from, but selecting the best model is limited to expert professionals, prone to user bias, and vulnerable to human error. Here we take the human out of the loop and automate the process of model discovery. Towards this goal, we establish a novel incompressible orthotropic constitutive neural network to simultaneously discover both, model and parameters, that best explain human cardiac tissue. Notably, our network features 32 individual terms, 8 isotropic and 24 anisotropic, and fully autonomously selects the best model, out of more than 4 billion possible combinations of terms. We demonstrate that we can successfully train the network with triaxial shear and biaxial extension tests and systematically sparsify the parameter vector withL1-regularization. Strikingly, we robustly discover a four-term model that features a quadratic term in the second invariantI2, and exponential quadratic terms in the fourth and eighth invariantsI4f,I4n, andI8fs. Importantly, our discovered model is interpretable by design and has parameters with well-defined physical units. We show that it outperforms popular existing myocardium models and generalizes well, from homogeneous laboratory tests to heterogeneous whole heart simulations. This is made possible by a new universal material subroutine that directly takes the discovered network weights as input. Automating the process of model discovery has the potential to democratize cardiac modeling, broaden participation in scientific discovery, and accelerate the development of innovative treatments for cardiovascular disease.Our source code, data, and examples are available athttps://github.com/LivingMatterLab/CANN.

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Section: Motivationmentioning

confidence: 99%

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Martonová,

Peirlinck,

Linka

et al. 2024

Preprint

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“…Massive advancements in data science are now bringing us closer than ever towards this goal 1,2 . Throughout the past three years, numerous research groups have begun to harness the potential of neural networks and fit constitutive models to experimental data, 3–14 an approach that is now widely known as constitutive neural networks 15 . While initial studies have used neural networks exclusively as black box regression operators, 16 recent approaches are increasingly recognizing their potential to discover not only the model parameters, but also the model itself 17 .…”

Section: Motivationmentioning

confidence: 99%

On sparse regression, L_p‐regularization, and automated model discovery

McCulloch,

St. Pierre,

Linka

et al. 2024

Numerical Meth Engineering

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Sparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the statistical tools for model discovery are well established in the context of linear regression, their generalization to nonlinear regression in material modeling is highly problem‐specific and insufficiently understood. Here we explore the potential of neural networks for automatic model discovery and induce sparsity by a hybrid approach that combines two strategies: regularization and physical constraints. We integrate the concept of Lp regularization for subset selection with constitutive neural networks that leverage our domain knowledge in kinematics and thermodynamics. We train our networks with both, synthetic and real data, and perform several thousand discovery runs to infer common guidelines and trends: L2 regularization or ridge regression is unsuitable for model discovery; L1 regularization or lasso promotes sparsity, but induces strong bias that may aggressively change the results; only L0 regularization allows us to transparently fine‐tune the trade‐off between interpretability and predictability, simplicity and accuracy, and bias and variance. With these insights, we demonstrate that Lp regularized constitutive neural networks can simultaneously discover both, interpretable models and physically meaningful parameters. We anticipate that our findings will generalize to alternative discovery techniques such as sparse and symbolic regression, and to other domains such as biology, chemistry, or medicine. Our ability to automatically discover material models from data could have tremendous applications in generative material design and open new opportunities to manipulate matter, alter properties of existing materials, and discover new materials with user‐defined properties.

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“…Thus, all quantities in the co-rotated intermediate configuration are uniquely defined and can be implemented directly using automated differentiation tools such as Ace Gen [19,20]. For a more detailed discussion on this topic, the reader is referred to [21].…”

Section: Inelastic Materials Formulationmentioning

confidence: 99%

A constitutive model for describing decoupled material behavior in thickness and in‐plane directions

Boes,

Simon,

Holthusen

2023

Proc Appl Math and Mech

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An increasing demand for paper and paperboard in engineering applications has emerged throughout the years. This leads to a growing interest in simulation tools to predict the material behavior, which is challenging due to the anisotropic structure of the material. It can be divided into in‐plane and out‐of‐plane behavior, which is mostly independent of each other resulting from the microstructure. Thus, a constitutive material model that captures in‐plane and out‐of‐plane behavior in a consistent manner is desired to simulate complex deformation states. The decoupling will be incorporated by a decomposition of the kinematics and the energy formulation into in‐plane and out‐of‐plane terms by use of structural tensors. This approach is flexible and can easily be extended to inelastic material behavior. In this work, the introduction of the decoupling into a constitutive material model for inelastic behavior is described. Visco‐elasticity is included through inelastic potentials. Three different potential formulations are given where focus is on the third, novel formulation, which defines inelastic strain evolution only in out‐of‐plane directions. The capabilities of this formulation are compared to the remaining potentials by simulations of a pinched cylinder that is loaded in the out‐of‐plane direction.

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Inelastic material formulations based on a co-rotated intermediate configuration—Application to bioengineered tissues

Cited by 22 publications

References 124 publications

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

On sparse regression, L_p‐regularization, and automated model discovery

A constitutive model for describing decoupled material behavior in thickness and in‐plane directions

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Inelastic material formulations based on a co-rotated intermediate configuration—Application to bioengineered tissues

Cited by 22 publications

References 124 publications

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

On sparse regression, Lp‐regularization, and automated model discovery

A constitutive model for describing decoupled material behavior in thickness and in‐plane directions

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Product

Resources

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On sparse regression, L_p‐regularization, and automated model discovery