mlsanityData to 7 Oct 2026

Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINN

arXiv 2304.06044 ↗First posted 10 Apr 2023cs.CE cs.AI cs.LGcited by 6

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Abstract (arXiv)

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides information about the current material state (i.e., free energy, stress, and the evolution of internal variables) under any given loading scenario without requiring initial data. One advantage of this work is that it bypasses the repetitive Newton iterations needed to solve nonlinear equations in complex material models. Additionally, strategies are provided to reduce the required order of derivative for obtaining the tangent operator. The trained model can be directly used in any finite element package (or other numerical methods) as a user-defined material model. However, challenges remain in the proper definition of collocation points and in integrating several non-equality constraints that become active or non-active simultaneously. We tested this methodology on rate-independent processes such as the classical von Mises plasticity model with a nonlinear hardening law, as well as local damage models for interface cracking behavior with a nonlinear softening law. In order to demonstrate the applicability of the methodology in handling complex path dependency in a three-dimensional (3D) scenario, we tested the approach using the equations governing a damage model for a three-dimensional interface model. Such models are frequently employed for intergranular fracture at grain boundaries. We have observed a perfect agreement between the results obtained through the proposed methodology and those obtained using the classical approach. Furthermore, the proposed approach requires significantly less effort in terms of implementation and computing time compared to the traditional methods.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 31 of its 79 references that are in the map. First posted on arXiv 10 Apr 2023.

Builds on

31 of 79 references.

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19 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 2; 2026: 1.

6 papers.

  1. 2024A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformationscited by 10
  2. 2024EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomialscited by 9
  3. 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
  4. 2025Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learningcited by 6
  5. 2025Neuro-Spectral Architectures for Causal Physics-Informed Networkscited by 3
  6. 2026Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damagecited by 0