Sign in Subscribe
Artificial neural networks

Generalized Standard Material Networks: A Machine Learning Framework for Understanding Material Behavior

Strategic Insights

— 2 min read

Researchers at Friedrich-Alexander-University Erlangen-Nurnberg (FAU) have developed a novel machine learning framework called Generalized Standard Material Networks, which utilizes convex neural networks to learn the mechanical behavior of complex materials. This framework, supported by the European Research Council (ERC), SNF, Switzerland, and the German Research Foundation (DFG), aims to provide a unified and overarching approach to describe a wide range of material behaviors, including elastic, viscoelastic, plastic, and viscoplastic responses with hardening.

Key Takeaways:

  • The Generalized Standard Material Networks framework uses convex neural networks to learn the mechanical behavior of complex materials, ensuring thermodynamic consistency.
  • The framework proposes the existence of two thermodynamic potentials, the Helmholtz free energy density and the dissipation rate density potential, which determine the constitutive material response.
  • The researchers parameterize these potentials with two artificial neural networks, satisfying all necessary properties by construction.
  • Using automatic differentiation, implicit time integration, and the Newton-Raphson method, the framework can describe a multitude of material behaviors within a single unified framework.
  • The researchers demonstrated satisfactory prediction accuracy and high robustness to noise on synthetic data generated by five benchmark material models.
  • A carefully chosen number of internal variables is shown to strike a balance between fitting accuracy and model complexity.
  • Additional authors of this research include Paul Steinmann, Ellen Kuhl, and Laura De Lorenzis.

Statistics:

  • The research was supported by the European Research Council (ERC), SNF, Switzerland, and the German Research Foundation (DFG).
  • The framework consists of two artificial neural networks, each parameterizing one of the two thermodynamic potentials.
  • The researchers used automatic differentiation, implicit time integration, and the Newton-Raphson method to describe material behavior.
  • Five benchmark material models were used to generate synthetic data for testing the framework.
  • A carefully chosen number of internal variables (10) strikes a balance between fitting accuracy and model complexity.
  • The research was peer-reviewed and published in the Journal of the Mechanics and Physics of Solids, 2025;200.

Sources:

  • Convex Neural Networks Learn Generalized Standard Material Models. Journal of the Mechanics and Physics of Solids, 2025;200.
  • Journal of the Mechanics and Physics of Solids: Pergamon-elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, England (Elsevier - www.elsevier.com; Journal of the Mechanics and Physics of Solids - www.journals.elsevier.com/journal-of-the-mechanics-and-physics-of-solids/)
  • NewsRx. New Mechanics and Physics of Solids Findings from Friedrich-Alexander-University Erlangen-Nurnberg (FAU) Outlined (Convex Neural Networks Learn Generalized Standard Material Models). Journal of Physics Research. July 8, 2025; p 368.

Read more