A data‐driven bond‐based peridynamic model derived from group method of data handling neural network with genetic algorithm

In the governing equation of motion of bond‐based peridynamics, the acceleration of a material point can be considered as the response function of all the displacements of material points in the horizon and a micro stiffness containing Young's modulus and length scale. A group method of data ha...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 123; no. 22; pp. 5618 - 5651
Main Authors: Yu, Xiang‐Long, Zhou, Xiao‐Ping
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 30.11.2022
Wiley Subscription Services, Inc
Subjects:
data‐driven model
Elastic deformation
equation of motion
Equations of motion
Exact solutions
Finite element method
Genetic algorithms
GMDH neural network
Group method of data handling
Horizon
Modulus of elasticity
Neural networks
peridynamics
Response functions
Stiffness
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:In the governing equation of motion of bond‐based peridynamics, the acceleration of a material point can be considered as the response function of all the displacements of material points in the horizon and a micro stiffness containing Young's modulus and length scale. A group method of data handling (GMDH) neural network is first developed to explicitly derive the discrete bond‐based peridynamic equation of motion based on measured data in this study rather than traditional complicated mathematical derivation. In order to discover the optimal structure more efficiently and to avoid exhaustive search, genetic algorithm is incorporated into GMDH structure. It is found that the prediction results obtained by GMDH model agree well with measured values both for training and testing data. Moreover, the derived equation of motion is expressed as the product of parameter composed of Young's modulus and length scale and linear combination of displacements of material points in the horizon, which is in accordance with the original bond‐based peridynamic formulation. Furthermore, numerical benchmarks associated with elastic deformation and crack problems are performed and compared with analytical solution or finite element analysis result to verify the validity and feasibility of the proposed model.
Bibliography:Funding information
National Natural Science Foundation of China
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.7081