Inference of deformation mechanisms and constitutive response of soft material surrogates of biological tissue by full-field characterization and data-driven variational system identification

Wang, Z.; Estrada, Jonathan B.; Arruda, Ellen M.; Garikipati, Krishna

doi:10.1016/j.jmps.2021.104474

Cited by 32 publications

(30 citation statements)

References 38 publications

(53 reference statements)

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“…• The anisotropic features -similar to isotropic generalized Mooney-Rivlin features -are based on monomials of J 4 and J 6 (Wang et al, 2021). Although polynomial terms up to fourth order are considered here for illustrative purposes, higher order terms can be used to obtain a more accurate surrogate for complicated anisotropic models like the Holzapfel model (Holzapfel et al, 2000).…”

Section: Constitutive Model Librarymentioning

confidence: 99%

“…Compared to the previous work by Flaschel et al (2021) and Wang et al (2021), the library includes a more diverse set of features beyond isotropic and polynomial features; the positivity constraint on θ ensures that all solutions found are automatically physically admissible. We note that the method is not limited to the feature library chosen here and can be extended to include any additional features based on prior knowledge about the material system.…”

Section: Constitutive Model Librarymentioning

confidence: 99%

“…The problem has been classically addressed via sparse regression (Brunton et al, 2016) -which is based on iterative minimization of an objective function in a non-probabilistic setting with lasso, ridge, or similar parsimony-inducing regularization. The resulting discovered constitutive models are of deterministic nature (Flaschel et al, 2021;Wang et al, 2021).…”

Section: Model Prior With Parsimony Biasmentioning

confidence: 99%

“…In light of the above challenges, previous work (Flaschel et al, 2021) by some of the authors and independently by Wang et al (2021) presented a method to neither surrogate nor bypass, but rather automatically discover interpretable constitutive models of hyperelastic materials from full-field displacement data and global reaction forces. More recently, the approach was extended to plasticity (Flaschel et al, 2022) and denoted as Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Joshi,

Thakolkaran,

Zheng

et al. 2022

Preprint

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Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to realistically measurable full-field displacement and global reaction force data; as opposed to calibration of an a priori assumed model, we start with a constitutive model ansatz based on a large catalog of candidate functional features; we leverage domain knowledge by including features based on existing, both physics-based and phenomenological, constitutive models. In the new Bayesian-EUCLID approach, we use a hierarchical Bayesian model with sparsitypromoting priors and Monte Carlo sampling to efficiently solve the parsimonious model selection task and discover physically consistent constitutive equations in the form of multivariate multi-modal probabilistic distributions. We demonstrate the ability to accurately and efficiently recover isotropic and anisotropic hyperelastic models like the Neo-Hookean, Isihara, Gent-Thomas, Arruda-Boyce, Ogden, and Holzapfel models in both elastostatics and elastodynamics. The discovered constitutive models are reliable under both epistemic uncertainties -i.e. uncertainties on the true features of the constitutive catalog -and aleatoric uncertainties -which arise from the noise in the displacement field data, and are automatically estimated by the hierarchical Bayesian model.

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Section: Constitutive Model Librarymentioning

confidence: 99%

Section: Constitutive Model Librarymentioning

confidence: 99%

Section: Model Prior With Parsimony Biasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Joshi,

Thakolkaran,

Zheng

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…First, there is an experimental optimization consideration. Techniques that leverage the weak form formulation of mechanical equilibrium-namely, those that employ measurement of fullfield deformations of some sort such as the virtual fields method [4], finite element model updating [5], or variational system identification as in our own work [6]-benefit from multiple types of deformation occurring in one sample simultaneously. However, approaches to evaluate the representation of deformation types in an intentionally heterogeneous experiment often do so in terms of invariant quantities I 1 and I 2 of either the left or right Cauchy-Green tensor [7].…”

Section: Introductionmentioning

confidence: 99%

Ogden Material Calibration via Magnetic Resonance Cartography, Parameter Sensitivity, and Variational System Identification

Nikolov¹,

Srivastava²,

Abeid³

et al. 2022

Preprint

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Contemporary techniques in the mechanical calibration of materials that leverage full three-dimensional deformation fields and the weak form of the equilibrium equations face challenges in the numerical solving procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying their system mechanics. The widely-used Ogden material model, comprised of an unknown number of terms of the same mathematical form, presents challenges in interpretability, stability, and parsimony. In turn, we intend to use our estimates to assess and improve our experimental design. Using fully 3D displacement fields acquired in silicone elastomers using our recently-developed magnetic resonance cartography (MR-u) technique on the order of > 20, 000 points per sample, we leverage PDE-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new decomposition of the deformation field locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric, and discuss the implications for future experimental design.

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Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

Bahmani,

Sun

2024

Numerical Meth Engineering

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We present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose a polyconvex neural additive model (PNAM) that enables us to express the hyperelastic model in a learnable feature space while enforcing polyconvexity. An upshot of this feature space obtained via the PNAM is that (1) it is spanned by a set of univariate basis functions that can be re‐parametrized with a more complex mathematical form, and (2) the resultant elasticity model is guaranteed to fulfill the polyconvexity, which ensures that the acoustic tensor remains elliptic for any deformation. To further improve the interpretability, we use genetic programming to convert each univariate basis into a compact mathematical expression. The resultant multi‐variable mathematical models obtained from this proposed framework are not only more interpretable but are also proven to fulfill physical laws. By controlling the compactness of the learned symbolic form, the machine learning‐generated mathematical model also requires fewer arithmetic operations than its deep neural network counterparts during deployment. This latter attribute is crucial for scaling large‐scale simulations where the constitutive responses of every integration point must be updated within each incremental time step. We compare our proposed model discovery framework against other state‐of‐the‐art alternatives to assess the robustness and efficiency of the training algorithms and examine the trade‐off between interpretability, accuracy, and precision of the learned symbolic hyperelastic models obtained from different approaches. Our numerical results suggest that our approach extrapolates well outside the training data regime due to the precise incorporation of physics‐based knowledge.

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Inference of deformation mechanisms and constitutive response of soft material surrogates of biological tissue by full-field characterization and data-driven variational system identification

Cited by 32 publications

References 38 publications

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Ogden Material Calibration via Magnetic Resonance Cartography, Parameter Sensitivity, and Variational System Identification

Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

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