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Model-Free Data-Driven Inelasticity

arXiv 1808.10859 ↗First posted 31 Aug 2018cs.CE physics.comp-phcited by 29

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Abstract (arXiv)

We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: i) materials with memory, i.e., conditioning the material data set to the past history of deformation; ii) differential materials, i.e., conditioning the material data set to short histories of stress and strain; and iii) history variables, i.e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of Data-Driven inelasticity and the numerical performance of implementations thereof.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Aug 2018.

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Citing papers per year: 2021: 4; 2022: 7; 2023: 9; 2024: 3; 2025: 4; 2026: 2.

29 papers.

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  1. 2024A review on data-driven constitutive laws for solidscited by 35
  2. 2022NN-EUCLID: deep-learning hyperelasticity without stress datacited by 30
  3. 2021The mixed deep energy method for resolving concentration features in finite strain hyperelasticitycited by 28
  4. 2022Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materialscited by 18
  5. 2022Modular machine learning-based elastoplasticity: generalization in the context of limited datacited by 16
  6. 2022A physics-informed deep neural network for surrogate modeling in classical elasto-plasticitycited by 15
  7. 2023Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Reviewcited by 15
  8. 2022Deep autoencoders for physics-constrained data-driven nonlinear materials modelingcited by 13
  9. 2023Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticitycited by 13
  10. 2025Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)cited by 13
  11. 2022Calibrating constitutive models with full-field data via physics informed neural networkscited by 12
  12. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
17 more
  1. 2022Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticitycited by 11
  2. 2021Model-data-driven constitutive responses: application to a multiscale computational frameworkcited by 6
  3. 2023LS-DYNA Machine Learning-based Multiscale Method for Nonlinear Modeling of Short Fiber-Reinforced Compositescited by 6
  4. 2023Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINNcited by 6
  5. 2023A Multi-Resolution Physics-Informed Recurrent Neural Network: Formulation and Application to Musculoskeletal Systemscited by 6
  6. 2025Learning Memory and Material Dependent Constitutive Lawscited by 5
  7. 2025History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materialscited by 5
  8. 2023Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanicscited by 4
  9. 2021Cell division in deep material networks applied to multiscale strain localization modelingcited by 2
  10. 2021Manifold embedding data-driven mechanicscited by 2
  11. 2024Machine Learning Aided Modeling of Granular Materials: A Reviewcited by 2
  12. 2025Beyond empirical models: Discovering new constitutive laws in solids with graph-based equation discoverycited by 2
  13. 2024N-Adaptive Ritz Method: A Neural Network Enriched Partition of Unity for Boundary Value Problemscited by 1
  14. 2023Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Methodcited by 0
  15. 2023PerSival: Neural-network-based visualisation for pervasive continuum-mechanical simulations in musculoskeletal biomechanicscited by 0
  16. 2026Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modelingcited by 0
  17. 2026Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damagecited by 0