Data-driven modeling of the mechanical behavior of anisotropic soft biological tissue

Taç, Vahidullah; Sree, Vivek D.; Rausch, Manuel K.; Tepole, Adrián Buganza

doi:10.1007/s00366-022-01733-3

Cited by 30 publications

(21 citation statements)

References 58 publications

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“… while all other network parameters train to zero. Unlike in classical neural networks, for which the weights have no physical interpretation [50, 51], our non-zero weights w 0 = 1.5708, w 1,4 = 0.8207, w 2,4 = 0.8097 MPa, w 1,12 = 0.3921, w 2,12 = 0.3388 MPa, naturally translate into a set of meaningful, physically interpretable parameters: a collagen fiber angle of α = 90 0 , matrix and fiber stiffnesses of a 1 = 1.3291 MPa and a 4 = 0.2656 MPa, and matrix and fiber coefficients of b 1 = 0.8207 and b 4 = 0.3921, that can teach us something about the underlying microstructure and physics of skin [30].…”

Section: Discussionmentioning

confidence: 99%

“…The first pioneering biaxial test system for skin was proposed almost five decades ago [23], and has since then become the method of choice to characterize flat composite materials with stiff fibers embedded in a soft matrix. Instead of data pairs, this system provides data triplets, { λ x , σ xx , σ yy } and { λ y , σ xx , σ yy }, where the second stretch λ y or λ x is either held constant or increased as a function of λ x or λ y [24, 25, 50, 51]. From Figure 3 for rabbit skin and Figure 6 for pig skin, we conclude that this method provides rich enough data to discover both a unique model and a parameter set, even from single experiments.…”

Section: Discussionmentioning

confidence: 99%

“…We compare the stress-stretch relations (19) with recent biaxial extension experiments on pig skin [50, 51]. These experiments include five sets of biaxial extension tests with prescribed stretch pairs, strip-x with λ 2 = 1.000, off-x with , equi-biaxial with λ 2 = λ 1 , off-y with , and strip-y with λ 1 = 1.000.…”

Section: Biaxial Extension Testsmentioning

confidence: 99%

See 2 more Smart Citations

Automated model discovery for skin: Discovering the best model, data, and experiment

Linka

Tepole

Holzapfel

et al. 2022

Preprint

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Choosing the best constitutive model and the right set of model parameters is at the heart of continuum mechanics. For decades, the gold standard in constitutive modeling has been to first select a model and then fit its parameters to data. However, the success of this approach is highly dependent on user experience and personal preference. Here we propose a new method that simultaneously and fully autonomously discovers the best model and parameters to explain experimental data. Mathematically, the model finding is translated into a complex non-convex optimization problem. We solve this problem by formulating it as a neural network, and leveraging the success, robustness, and stability of the optimization tools developed in classical neural network modeling. Instead of using a classical off-the-shelf neural network, we design a new family of Constitutive Artificial Neural Networks with activation functions that feature popular constitutive models and parameters that have a clear physical interpretation. Our new network inherently satisfies general kinematic, thermodynamic, and physical constraints and trains robustly, even with sparse data. We illustrate its potential for biaxial extension experiments on skin and demonstrate that the majority of network weights train to zero, while the small subset of non-zero weights defines the discovered model. Unlike classical network weights, these weights are physically interpretable and translate naturally into engineering parameters and microstructural features such as stiffness and fiber orientation. Our results suggest that Constitutive Artificial Neural Networks enable automated model, parameter, and experiment discovery and could initiate a paradigm shift in constitutive modeling, from user-defined to automated model selection and parameterization.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Automated model discovery for skin: Discovering the best model, data, and experiment

Linka

Tepole

Holzapfel

et al. 2022

Preprint

Self Cite

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show abstract

“…Probably, the most common tech-nique is the application of artificial neural networks (ANNs), which have already been proposed in the early 90s by the pioneering work of Ghabussi et al [28]. In the last decades, ANNs have been intensively used for mechanical material modeling and simulations by means of the finite element method (FEM), e. g., in [4,33,38,71,73,86] among others.…”

Section: Overview On Data-based Constitutive Modelingmentioning

confidence: 99%

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

et al. 2023

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Herein, we present a new data-driven multiscale framework called FE$${}^\textrm{ANN}$$ ANN which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous data mining process. Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. Thereby, we restrict ourselves to finite strain hyperelasticity problems for now. By using a set of problem specific invariants as the input of the ANN and the Helmholtz free energy density as the output, several physical principles, e. g., objectivity, material symmetry, compatibility with the balance of angular momentum and thermodynamic consistency are fulfilled a priori. The necessary data for the training of the ANN-based surrogate model, i. e., macroscopic deformations and corresponding stresses, are collected via computational homogenization of representative volume elements (RVEs). Thereby, the core feature of the approach is given by a completely autonomous mining of the required data set within an overall loop. In each iteration of the loop, new data are generated by gathering the macroscopic deformation states from the macroscopic finite element simulation and a subsequently sorting by using the anisotropy class of the considered material. Finally, all unknown deformations are prescribed in the RVE simulation to get the corresponding stresses and thus to extend the data set. The proposed framework consequently allows to reduce the number of time-consuming microscale simulations to a minimum. It is exemplarily applied to several descriptive examples, where a fiber reinforced composite with a highly nonlinear Ogden-type behavior of the individual components is considered. Thereby, a rather high accuracy could be proved by a validation of the approach.

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“…Furthermore, closed-form models inherently restrict the type of behaviors that can be described, often rendering them incapable of accurately capturing the response of many materials. Both of these problems can be solved with the help of data-driven methods as has been demonstrated various times for the case of hyperelasticity [3,4,5,6], but remains an ongoing area of investigation for dissipative phenomena such as viscoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Anisotropic Finite Viscoelasticity Using Neural Ordinary Differential Equations

Taç

Rausch

Costabal

et al. 2023

Preprint

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Data-driven modeling of the mechanical behavior of anisotropic soft biological tissue

Cited by 30 publications

References 58 publications

Automated model discovery for skin: Discovering the best model, data, and experiment

Automated model discovery for skin: Discovering the best model, data, and experiment

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

Data-Driven Anisotropic Finite Viscoelasticity Using Neural Ordinary Differential Equations

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