Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

Gärtner, Til; Fernández, Mauricio; Weeger, Oliver

doi:10.1007/s00466-021-02061-x

Cited by 19 publications

(6 citation statements)

References 66 publications

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“…Recently, we and other research groups have developed constitutive models based on DNNs [45][46][47][48][49][50][51], which perform better than the expert-prescribed models in some applications. However, it can be difficult to implement a complex DNN as a user subroutine in the programming language that is compatible with commercial software packages, e.g., FORTRAN for Abaqus UMAT.…”

Section: Discussionmentioning

confidence: 99%

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Liang

Liu

Elefteriades

et al. 2023

Preprint

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Motivation: Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed. Methods: In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance. Results: We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.

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Section: Discussionmentioning

confidence: 99%

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Liang

Liu

Elefteriades

et al. 2023

Preprint

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“…Regarding the introduced new family of NN-based hyperelastic models, which fulfill all of the aforementioned conditions in an exact way, we advocate for naming them as physics-augmented neural networks (PANNs). The proposed framework will be very valuable in fields, where highly flexible and at the same time physically sensible constitutive models are required, such as the simulation of microstructured materials [14,19]. For this purpose, the PANN approach is build up by extending the aforementioned model [24] by polyconvex normalization terms, followed by a detailed analytical and numerical study analyzing the overall model.…”

Section: Introductionmentioning

confidence: 99%

Neural networks meet hyperelasticity: A guide to enforcing physics

Linden¹,

Klein²,

Kalina³

et al. 2023

Preprint

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In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using different sets of invariants as inputs, a hyperelastic potential is formulated as a convex neural network, thus fulfilling symmetry of the stress tensor, objectivity, material symmetry, polyconvexity, and thermodynamic consistency. In addition, a physically sensible stress behavior of the model is ensured by using analytical growth terms, as well as normalization terms which ensure the undeformed state to be stress free and with zero energy. The normalization terms are formulated for both isotropic and transversely isotropic material behavior and do not violate polyconvexity. By fulfilling all of these conditions in an exact way, the proposed physics-augmented model combines a sound mechanical basis with the extraordinary flexibility that neural networks offer. Thus, it harmonizes the theory of hyperelasticity developed in the last decades with the up-to-date techniques of machine learning. Furthermore, the non-negativity of the hyperelastic potential is numerically verified by sampling the space of admissible deformations states, which, to the best of the authors' knowledge, is the only possibility for the considered nonlinear compressible models. The applicability of the model is demonstrated by calibrating it on data generated with analytical potentials, which is followed by an application of the model to finite element simulations. In addition, an adaption of the model to noisy data is shown and its extrapolation capability is compared to models with reduced physical background. Within all numerical examples, excellent and physically meaningful predictions have been achieved with the proposed physicsaugmented neural network.

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“…The second kind of model is established according to the deformation mechanism of the material, and the microscopic aspects, such as dislocation accumulation and grain size evolution, are considered [30][31][32]. The third kind of constitutive model can obtain the material constants using regression analysis and is used by many researchers due to its high prediction accuracy [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

The hot deformation behaviors and constitutive modeling of Hastelloy C276

Jiang²,

Deng³

et al. 2023

Mater. Res. Express

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Hastelloy C276 is widely used in the new generation of nuclear power plants, and hot deformation is the optimum way to form the C276 part. In this investigation, the hot deformation and constitutive modeling of Hastelloy C276 alloy are researched, and the processing maps are drawn. The results show that strain rate and hot deformation temperature have remarkable impacts on the deformation behaviors of the Hastelloy C276 alloy. The yield behavior and the flow stress are predicted based on the Arrhenius constitutive equation, and the correlation coefficients are 0.9613 and 0.9837, indicating the high prediction ability of the established constitutive equation. Rising the temperature can decrease the unstable deformation area, and the studied alloy can be deformed at low strain rates. With the increased strain rate, flow localization occurs, which is not suitable for hot deformation.

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Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

Cited by 19 publications

References 66 publications

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Neural networks meet hyperelasticity: A guide to enforcing physics

The hot deformation behaviors and constitutive modeling of Hastelloy C276

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