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A review on data-driven constitutive laws for solids

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arxiv 2405.03658 v1 pith:PTRU7CHS submitted 2024-05-06 cs.CE cs.LGphysics.app-ph

classification cs.CEcs.LGphysics.app-ph
keywords techniquesconstitutivedatadata-drivenlawsreviewsolidsacross
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This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits and drawbacks of the various techniques for interpreting and forecasting mechanics behavior across different scales. Distinguishing between machine-learning-based and model-free methods, we further categorize approaches based on their interpretability and on their learning process/type of required data, while discussing the key problems of generalization and trustworthiness. We attempt to provide a road map of how these can be reconciled in a data-availability-aware context. We also touch upon relevant aspects such as data sampling techniques, design of experiments, verification, and validation.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models

    cond-mat.mtrl-sci 2026-02 conditional novelty 6.0 of 10

    iCKAN combines input-convex Kolmogorov-Arnold networks with a thermodynamic inelasticity framework to turn stress-strain data into symbolic elastic and inelastic potentials.

  2. A Physics-Informed Data-Driven Discovery for Constitutive Modeling of Compressible, Nonlinear, History-Dependent Soft Materials under Multiaxial Cyclic Loading

    cond-mat.soft 2025-07 conditional novelty 6.0 of 10

    A hybrid GPR-LSTM model trained on synthetic Holzapfel viscoelastic data reproduces and extrapolates multiaxial cyclic stress response while keeping dissipation non-negative.

  3. Mixing Data-Driven and Physics-Based Constitutive Models using Uncertainty-Driven Phase Fields

    math.NA 2025-04 conditional novelty 6.0 of 10

    A phase field driven by Gaussian process uncertainty dynamically mixes a data-driven surrogate with a high-fidelity elasto-plastic constitutive model, reducing high-fidelity evaluations while preserving accuracy.

  4. Stress Softening Damage in Strongly Nonlinear Viscoelastic Soft Materials A Physics Informed Data Driven Constitutive Model with Time Temperature Coupling

    cond-mat.soft 2025-07 reject novelty 5.0 of 10

    A physics-informed TCN surrogate is trained on synthetic thermo-viscoelastic data with Mullins damage and reportedly generalizes to unseen stretch, rate, and temperature conditions, though validation stays within the ...

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