Meshless physics‐informed deep learning method for three‐dimensional solid mechanics

Deep learning (DL) and the collocation method are merged and used to solve partial differential equations (PDEs) describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo‐Hookean) with large deformation, and von Mises plasticity...

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Veröffentlicht in:International journal for numerical methods in engineering Jg. 122; H. 23; S. 7182 - 7201
Hauptverfasser: Abueidda, Diab W., Lu, Qiyue, Koric, Seid
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken, USA John Wiley & Sons, Inc 15.12.2021
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Schlagworte:
Collocation methods
computational mechanics
Deep learning
Deformation
Finite element method
machine learning
Mathematical models
meshfree method
Meshless methods
Neural networks
Numerical methods
Partial differential equations
physics‐informed learning
Solid mechanics
ISSN:0029-5981, 1097-0207
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Zusammenfassung:Deep learning (DL) and the collocation method are merged and used to solve partial differential equations (PDEs) describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo‐Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening. The performance of this deep collocation method (DCM) depends on the architecture of the neural network and the corresponding hyperparameters. The presented DCM is meshfree and avoids any spatial discretization, which is usually needed for the finite element method (FEM). We show that the DCM can capture the response qualitatively and quantitatively, without the need for any data generation using other numerical methods such as the FEM. Data generation usually is the main bottleneck in most data‐driven models. The DL model is trained to learn the model's parameters yielding accurate approximate solutions. Once the model is properly trained, solutions can be obtained almost instantly at any point in the domain, given its spatial coordinates. Therefore, the DCM is potentially a promising standalone technique to solve PDEs involved in the deformation of materials and structural systems as well as other physical phenomena.
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6828