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Article
Mathematics, Interdisciplinary Applications
Martin Zlatić et al.
COMPUTATIONAL MECHANICS
(2023)
Review
Computer Science, Interdisciplinary Applications
Alexander Ricker et al.
Summary: Hyperelasticity is a common modeling approach used to replicate the nonlinear mechanical behavior of rubber materials at finite deformations. This manuscript provides an overview of suitable hyperelastic models for nine widely used rubber compounds, including both isochoric and volumetric behavior. It discusses the careful preparation of experimental data, including proper handling of preload in tests and verification of data consistency. The parameter identification process is also studied, including different formulations of the cost function and their effect on fitting results. Ultimately, this contribution serves as a guideline for experimental characterization, data processing, model selection, and parameter identification for both existing and new materials.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Kevin Linka et al.
Summary: For over a century, scientists from various fields have proposed different models to characterize the behavior of materials under mechanical loading. However, classical neural networks fail to consider previous research in constitutive modeling and have limitations in predicting behavior beyond the training data. In this study, a new family of Constitutive Artificial Neural Networks (CANN) is developed to overcome these limitations and satisfy physical constraints. CANN shows promise in automating model discovery and has the potential to revolutionize constitutive modeling.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Karl A. Kalina et al.
Summary: This study presents an ANN-based approach for modeling and simulating isotropic hyperelastic solids efficiently. By reducing the problem's dimensionality, a simplified model using deformation type invariants and stress coefficients is trained to achieve high accuracy in simulating three-dimensional samples.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Jan N. Fuhg et al.
Summary: This paper introduces a method that combines data-driven constitutive prediction and macroscopic calculations, ensuring prediction accuracy and reliability by using local approximate Gaussian process regression (laGPR). A modified Newton-Raphson approach specific to laGPR is proposed to solve the global structural problem.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Dominik K. Klein et al.
Summary: In this paper, two machine learning based constitutive models for finite deformations are proposed. They are hyperelastic, anisotropic, fulfill the polyconvexity condition, and have excellent predictive and generalization capabilities. The models are calibrated with challenging simulation data and show good results, demonstrating their reliability and applicability.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Engineering, Multidisciplinary
Faisal As'ad et al.
Summary: This paper proposes a mechanics-informed artificial neural network approach for learning constitutive laws of complex, nonlinear, elastic materials. The approach captures highly nonlinear strain-stress mappings while preserving fundamental principles of solid mechanics. It enforces physical constraints and demonstrates potential for multi-scale applications.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Nikolaos N. Vlassis et al.
Summary: This paper presents a machine learning framework for predicting the anisotropic elastic response of organic molecular crystals. By using a molecular dynamics simulation database, neural networks are trained with Sobolev norm and additional constraints through transfer learning technique to improve the accuracy and robustness of the models.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Shenglin Huang et al.
Summary: This paper proposes a thermodynamics-based learning strategy for non-equilibrium evolution equations using Onsager's variational principle. The method learns the free energy and dissipation potential from spatio-temporal measurements, and enforces the satisfaction of the second law of thermodynamics. The approach is demonstrated on three physical processes, showing its robustness and versatility.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Materials Science, Multidisciplinary
Prakash Thakolkaran et al.
Summary: In this study, a new approach for unsupervised learning of hyperelastic constitutive laws using physics-consistent deep neural networks is proposed. The approach uses only displacement and reaction force data, and leverages a physics-motivated loss function based on the conservation of linear momentum to guide the learning process. By employing a specially designed neural network architecture, multiple physical and thermodynamic constraints are automatically satisfied, and the constitutive laws can be accurately learned.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Engineering, Multidisciplinary
Vahidullah Tac et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Filippo Masi et al.
Summary: The mechanical behavior of inelastic materials with microstructure is complex and difficult to predict accurately using traditional methods. This paper proposes a Thermodynamics-based Artificial Neural Networks (TANN) approach for modeling such materials. Several examples demonstrate the high accuracy and physical consistency of TANN in predicting macroscopic and microscopic mechanical behavior.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
J. N. Fuhg et al.
Summary: In this study, a tensor-basis neural network model is proposed to accurately predict the mechanical response of materials, especially those with microstructure and anisotropy. Classical representation theory, novel neural network layers, and L1 regularization are utilized to construct the model.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Engineering, Multidisciplinary
Dominik K. Klein et al.
Summary: In this work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. The model formulates an internal energy density as a convex neural network using different sets of invariants as inputs. It demonstrates applicability and versatility through calibration on different materials data and effective modeling of composite materials.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Vahidullah Tac et al.
Summary: Deep neural networks are used in describing the mechanical behavior of soft tissues. They overcome the limitations of traditional constitutive models by predicting strain energy and its derivatives, and enforcing polyconvexity through physics-informed constraints. A multi-fidelity scheme combining experimental and analytical data yields the best performance.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mechanics
Peiyi Chen et al.
Summary: This study proposes a simple approach to rectify unconstrained neural networks for hyperelastic constitutive models to ensure mathematical well-posedness and physical consistency. By selecting a proper parameterization and enforcing polyconvexity, neural networks can be made admissible. The relevance of this formulation is demonstrated through analysis of digitally synthesized and experimental datasets for various materials, including soft biological tissues.
MECHANICS RESEARCH COMMUNICATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Mauricio Fernandez et al.
Summary: This study investigates the capabilities of anisotropic theory-based, purely data-driven, and hybrid approaches to model the homogenized behavior of cubic lattice metamaterials. The results show that the data-driven models can accurately reproduce simulation data and manifest lattice instabilities, achieving superior accuracy in additional test scenarios.
COMPUTATIONAL MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Nikolaos N. Vlassis et al.
Summary: This study introduces a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, and demonstrates that machine learning hardening laws can recover classical rules and discover new mechanisms, resulting in more robust and accurate forward predictions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Til Gaertner et al.
Summary: A sequential nonlinear multiscale method is proposed for simulating elastic metamaterials subjected to large deformations and instabilities. The method involves inducing buckling in cubic beam lattice unit cells through stochastic perturbation, training anisotropic effective constitutive models using artificial neural networks, and conducting macroscopic nonlinear finite element simulations. The approach accurately reproduces highly nonlinear behavior of 3D metamaterials at lesser computational effort.
COMPUTATIONAL MECHANICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Patrick Weber et al.
Summary: This paper presents a new approach to enhance neural network training with physical knowledge using constraint optimization techniques in computational mechanics for material behavior approximation. Specific constraints for hyperelastic materials are introduced to address issues like small training samples and noisy data. Experimental results demonstrate that training with physical constraints outperforms state-of-the-art techniques in terms of stability and convergence behavior within finite element simulations.
COMPUTATIONAL MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Moritz Flaschel et al.
Summary: The proposed method allows for unsupervised discovery of isotropic hyperelastic constitutive laws, delivering interpretable models through sparse regression and automatically determining penalty parameters in the regularization term.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Review
Physics, Applied
George Em Karniadakis et al.
Summary: Physics-informed learning seamlessly integrates data and mathematical models through neural networks or kernel-based regression networks for accurate inference of realistic and high-dimensional multiphysics problems. Challenges remain in incorporating noisy data seamlessly, complex mesh generation, and addressing high-dimensional problems.
NATURE REVIEWS PHYSICS
(2021)
Article
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Karl A. Kalina et al.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2020)
Article
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Nikolaos N. Vlassis et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Mathematics, Applied
Robert J. Martin et al.
ANALYSIS AND APPLICATIONS
(2019)
Article
Computer Science, Software Engineering
Breannan Smith et al.
ACM TRANSACTIONS ON GRAPHICS
(2018)
Article
Engineering, Multidisciplinary
David Yang Gao et al.
JOURNAL OF ELASTICITY
(2017)
Article
Computer Science, Interdisciplinary Applications
C. Zopf et al.
COMPUTERS & STRUCTURES
(2017)
Article
Engineering, Multidisciplinary
T. Kirchdoerfer et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2016)
Article
Computer Science, Interdisciplinary Applications
Julia Ling et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2016)
Article
Engineering, Multidisciplinary
B. A. Le et al.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2015)
Article
Mechanics
Christoph Naumann et al.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2015)
Article
Engineering, Multidisciplinary
Patrizio Neff et al.
JOURNAL OF ELASTICITY
(2015)
Article
Materials Science, Multidisciplinary
Stephan Lehmich et al.
MATHEMATICS AND MECHANICS OF SOLIDS
(2014)
Article
Engineering, Multidisciplinary
Christophe Geuzaine et al.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2009)
Article
Engineering, Civil
G. Liang et al.
ENGINEERING STRUCTURES
(2008)
Article
Materials Science, Multidisciplinary
J. Schroeder et al.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2008)
Article
Mathematics, Interdisciplinary Applications
RW Ogden et al.
COMPUTATIONAL MECHANICS
(2004)
Article
Polymer Science
Y Shen et al.
RUBBER CHEMISTRY AND TECHNOLOGY
(2004)
Article
Mechanics
J Schroder et al.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2003)