☆ 4.7 Article

A deep learning energy method for hyperelasticity and viscoelasticity

EUROPEAN JOURNAL OF MECHANICS A-SOLIDS (2022)

Journal

EUROPEAN JOURNAL OF MECHANICS A-SOLIDS

Volume 95, Issue -, Pages -

Publisher

ELSEVIER

DOI: 10.1016/j.euromechsol.2022.104639

Keywords

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

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Mechanics

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Abstract

In this study, the potential energy formulation and deep learning are merged to introduce the deep energy method, which shows potential for solving deformation problems in hyperelastic and viscoelastic materials.

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 selfcontained 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.

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