Study on Constitutive Relations and Boundary Value Problems of Granular Materials Based on Artificial Neural Networks

ZHANG Guangjiang; YANG Deze; CHU Xihua

doi:10.21656/1000-0887.440248

Volume 45 Issue 2

Feb. 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(2): 155-166

ZHANG Guangjiang, YANG Deze, CHU Xihua. Study on Constitutive Relations and Boundary Value Problems of Granular Materials Based on Artificial Neural Networks[J]. Applied Mathematics and Mechanics, 2024, 45(2): 155-166. doi: 10.21656/1000-0887.440248

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Study on Constitutive Relations and Boundary Value Problems of Granular Materials Based on Artificial Neural Networks

doi: 10.21656/1000-0887.440248

Department of Engineering Mechanics, Wuhan University, Wuhan 430072, P.R.China

Received Date: 2023-08-17
Rev Recd Date: 2023-09-27
Publish Date: 2024-02-01

Abstract

Abstract

Granular materials are widely used in engineering practice, where the numerical simulation of boundary value problems related to granular materials is of great significance. By the artificial neural network algorithm, the discrete element method based on discrete particle models and the finite element method based on continuous models were organically combined to solve the boundary value problems of granular materials. A new and complete model and the solution were formed, namely, the micro-macroscopic 2-scale model and its solution system for offline calculation of the meso model. Specifically, the principal stress, the principal strain, and the corresponding stress-strain matrix of a granular material were first obtained based on the discrete element method. Then an artificial neural network model was built in the main space to describe the constitutive relationship of the granular material by an artificial neural network algorithm. Finally, the artificial neural network model was imported into ABAQUS to solve the boundary value problem of the granular material with the user-defined material subroutine UMAT. Through the numerical tests of plate compression and slope stability, and the comparison with the solution results of the classical elastoplastic model, it is seen that the trained artificial neural network model can effectively reflect the constitutive relationship of granular materials, and can be used in practice to solve boundary value problems. The results show the feasibility of the solution scheme.
- granular material,
- artificial neural network,
- discrete element method,
- finite element method,
- boundary value problem

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References(22)

References

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