Tensor-based physics-encoded neural networks for modeling constitutive behavior of soil

Zhihui Wang, Roberto Cudmani, Andrés Alfonso Peña Olarte

Research output: Contribution to journalArticlepeer-review


Data-driven constitutive models are increasingly addressing non-elastic and three-dimensional scenarios. However, their robustness can be significantly impacted by the inadequate integration of physical information. Accordingly, this study introduces a tensor-based physics-encoded neural network to characterize the constitutive behavior of soil, exemplified by isotropic hypoplasticity with dependency on pressure and porosity. The framework ensures strict adherence to fundamental physical laws for small strain, rate-independent isotropic constitutive behavior. The network utilizes stress tensor invariants and soil state parameters (porosity) as inputs, and outputs crucial coefficients for the tensorial constitutive relations. The model has been calibrated using only symmetric triaxial test data (both drained and undrained). The effectiveness of the neural network-based constitutive model has been validated through simulations of drained and undrained triaxial tests under various initial conditions, as well as boundary value problems with complex loading. The results demonstrate that the proposed model offers the following distinguishing advantages: 1) Applicability to both two- and three-dimensional non-elastic cases, even when trained with two-dimensional data; 2) Strict adherence to fundamental physical laws, avoiding soft constraints; 3) An incremental, tensor-based architecture, suitable for integration in numerical software for boundary value problems.

Original languageEnglish
Article number106173
JournalComputers and Geotechnics
StatePublished - Jun 2024


  • Constitutive model
  • Data-driven computational mechanics
  • Neural network
  • Physics-Informed Machine Learning
  • Plastic model


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