mlsanityData to 14 Oct 2026

Theory and implementation of inelastic Constitutive Artificial Neural Networks

arXiv 2311.06380 ↗First posted 10 Nov 2023cs.LG cond-mat.mtrl-scicited by 12

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Abstract (arXiv)

Nature has always been our inspiration in the research, design and development of materials and has driven us to gain a deep understanding of the mechanisms that characterize anisotropy and inelastic behavior. All this knowledge has been accumulated in the principles of thermodynamics. Deduced from these principles, the multiplicative decomposition combined with pseudo potentials are powerful and universal concepts. Simultaneously, the tremendous increase in computational performance enabled us to investigate and rethink our history-dependent material models to make the most of our predictions. Today, we have reached a point where materials and their models are becoming increasingly sophisticated. This raises the question: How do we find the best model that includes all inelastic effects to explain our complex data? Constitutive Artificial Neural Networks (CANN) may answer this question. Here, we extend the CANNs to inelastic materials (iCANN). Rigorous considerations of objectivity, rigid motion of the reference configuration, multiplicative decomposition and its inherent non-uniqueness, restrictions of energy and pseudo potential, and consistent evolution guide us towards the architecture of the iCANN satisfying thermodynamics per design. We combine feed-forward networks of the free energy and pseudo potential with a recurrent neural network approach to take time dependencies into account. We demonstrate that the iCANN is capable of autonomously discovering models for artificially generated data, the response of polymers for cyclic loading and the relaxation behavior of muscle data. As the design of the network is not limited to visco-elasticity, our vision is that the iCANN will reveal to us new ways to find the various inelastic phenomena hidden in the data and to understand their interaction. Our source code, data, and examples are available at doi.org/10.5281/zenodo.10066805

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 27 of its 129 references that are in the map. First posted on arXiv 10 Nov 2023.

Builds on

27 of 129 references.

References · 27

  1. 2016Input Convex Neural Networkscited by 414
  2. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 210
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  5. 2020Physics-informed deep learning for incompressible laminar flowscited by 54
  6. 2020Unsupervised discovery of interpretable hyperelastic constitutive lawscited by 51
  7. 2022A new family of Constitutive Artificial Neural Networks towards automated model discoverycited by 49
  8. 2020Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacturecited by 48
  9. 2021Physics informed neural networks for continuum micromechanicscited by 46
  10. 2020Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imagingcited by 40
  11. 2022A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element methodcited by 33
  12. 2022Automated discovery of generalized standard material models with EUCLIDcited by 31
15 more
  1. 2018Model-Free Data-Driven Inelasticitycited by 29
  2. 2022Discovering plasticity models without stress datacited by 28
  3. 2021Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)cited by 18
  4. 2022Constitutive model characterization and discovery using physics-informed deep learningcited by 17
  5. 2023Data-driven anisotropic finite viscoelasticity using neural ordinary differential equationscited by 16
  6. 2022A physics-informed deep neural network for surrogate modeling in classical elasto-plasticitycited by 15
  7. 2023Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domainscited by 14
  8. 2021A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticitycited by 12
  9. 2022Automatic generation of interpretable hyperelastic material models by symbolic regressioncited by 12
  10. 2022Evolution TANN and the identification of internal variables and evolution equations in solid mechanicscited by 9
  11. 2020Model-free Data-Driven Computational Mechanics Enhanced by Tensor Votingcited by 7
  12. 2021A macroscopic approach for stress driven anisotropic growth in bioengineered soft tissuescited by 3
  13. 2021Model-free Data-Driven simulation of inelastic materials using structured data sets, tangent space information and transition rulescited by 2
  14. 2022A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementationcited by 2
  15. 2021A novel approach for the efficient modeling of material dissolution in electrochemical machiningcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 2; 2026: 7.

12 papers.

  1. 2024A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domainscited by 15
  2. 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
  3. 2024Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodelingcited by 6
  4. 2026Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material modelscited by 6
  5. 2025A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strainscited by 4
  6. 2025COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updatescited by 2
  7. 2026A Convex Route to Thermoelasticity: Learning Internal Energy and Dissipationcited by 1
  8. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  9. 2026LLM-driven design of physics-constrained constitutive models: two agents are better than onecited by 0
  10. 2026Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regressioncited by 0
  11. 2026Benchmarking data-driven material models on the classic Treloar datasetcited by 0
  12. 2026Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damagecited by 0