A novel neural network method for solid mechanics problems of heterogeneous bars.
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| Title: | A novel neural network method for solid mechanics problems of heterogeneous bars. |
|---|---|
| Authors: | Lanka, Mitra Ramakrishna1 (AUTHOR) lankamn@mail.uc.edu, Liu, Gui-Rong1 (AUTHOR) |
| Source: | Engineering Applications of Artificial Intelligence. Sep2025:Part A, Vol. 156, pN.PAG-N.PAG. 1p. |
| Subjects: | Domain decomposition methods, Boundary value problems, Solid mechanics, Finite element method, Inhomogeneous materials |
| Abstract: | This paper introduces a novel neural network (NN) method using Physics-Informed Neural Networks (PINNs) to solve boundary value problems in solid mechanics for heterogeneous materials. Existing domain decomposition methods in PINNs require multiple NNs and indiscriminate data sampling, often with heuristically chosen NN architectures. In contrast, this work proposes a domain variation strategy that solves heterogeneous problems using a single-hidden-layered NN. The strategy uses boundary, interface, and collocation spatial coordinates from all sub-domains to generate variations of the heterogeneous solid, which facilitates the establishment of mechanical connections within the NN. From each variation, a unique dataset is generated and fed into an instance of NN, referred to as sub-NN, which output displacements and their gradients. Outputs from all sub-NNs are utilized to compute boundary losses (via boundary conditions), interface losses (via continuity conditions), and governing equation losses, which are minimized using Adam and Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization methods. The number of data samples and optimal neurons for convergence are determined through theoretical studies. The method's effectiveness is demonstrated on a heterogeneous bar fixed at one end and subjected to a load at the other. Validation against Finite Element Method (FEM) simulations shows mean squared error (MSE) of 0.04, with a mean absolute percentage error (MAPE) of 4.64 % for the 20-material bar problem involving force variation. The NN model effectively captures displacements, stresses, and strain discontinuities at the material interfaces. This approach offers an efficient alternative to domain decomposition methods and a framework for solving multiple problems via surrogate modeling. [ABSTRACT FROM AUTHOR] |
| Copyright of Engineering Applications of Artificial Intelligence is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 185809129 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A novel neural network method for solid mechanics problems of heterogeneous bars. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lanka%2C+Mitra+Ramakrishna%22">Lanka, Mitra Ramakrishna</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lankamn@mail.uc.edu</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Gui-Rong%22">Liu, Gui-Rong</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Engineering+Applications+of+Artificial+Intelligence%22">Engineering Applications of Artificial Intelligence</searchLink>. Sep2025:Part A, Vol. 156, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+mechanics%22">Solid mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Inhomogeneous+materials%22">Inhomogeneous materials</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper introduces a novel neural network (NN) method using Physics-Informed Neural Networks (PINNs) to solve boundary value problems in solid mechanics for heterogeneous materials. Existing domain decomposition methods in PINNs require multiple NNs and indiscriminate data sampling, often with heuristically chosen NN architectures. In contrast, this work proposes a domain variation strategy that solves heterogeneous problems using a single-hidden-layered NN. The strategy uses boundary, interface, and collocation spatial coordinates from all sub-domains to generate variations of the heterogeneous solid, which facilitates the establishment of mechanical connections within the NN. From each variation, a unique dataset is generated and fed into an instance of NN, referred to as sub-NN, which output displacements and their gradients. Outputs from all sub-NNs are utilized to compute boundary losses (via boundary conditions), interface losses (via continuity conditions), and governing equation losses, which are minimized using Adam and Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization methods. The number of data samples and optimal neurons for convergence are determined through theoretical studies. The method's effectiveness is demonstrated on a heterogeneous bar fixed at one end and subjected to a load at the other. Validation against Finite Element Method (FEM) simulations shows mean squared error (MSE) of 0.04, with a mean absolute percentage error (MAPE) of 4.64 % for the 20-material bar problem involving force variation. The NN model effectively captures displacements, stresses, and strain discontinuities at the material interfaces. This approach offers an efficient alternative to domain decomposition methods and a framework for solving multiple problems via surrogate modeling. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Engineering Applications of Artificial Intelligence is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.engappai.2025.111084 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Domain decomposition methods Type: general – SubjectFull: Boundary value problems Type: general – SubjectFull: Solid mechanics Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Inhomogeneous materials Type: general Titles: – TitleFull: A novel neural network method for solid mechanics problems of heterogeneous bars. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lanka, Mitra Ramakrishna – PersonEntity: Name: NameFull: Liu, Gui-Rong IsPartOfRelationships: – BibEntity: Dates: – D: 09 M: 09 Text: Sep2025:Part A Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09521976 Numbering: – Type: volume Value: 156 Titles: – TitleFull: Engineering Applications of Artificial Intelligence Type: main |
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