A deep learning energy method for hyperelasticity and viscoelasticity

Diab W. Abueidda, Seid Koric, Rashid Abu Al-Rub, Corey M. Parrott, Kai A. James, Nahil A. Sobh

Research output: Contribution to journalArticlepeer-review


The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and meshfree. It can accurately capture the three-dimensional (3D) mechanical response without requiring any time-consuming training data generation by classical numerical methods such as the finite element method. Once the model is appropriately trained, the response can be attained almost instantly at any point in the physical domain, given its spatial coordinates. Therefore, the deep energy method is potentially a promising standalone method for solving partial differential equations describing the mechanical deformation of materials or structural systems and other physical phenomena.

Original languageEnglish (US)
Article number104639
JournalEuropean Journal of Mechanics, A/Solids
StatePublished - Sep 1 2022


  • Computational mechanics
  • Finite deformation
  • Meshfree method
  • Neural networks
  • Partial differential equations
  • Physics-informed learning

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy


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