Dissertation/ Thesis
Learning Non-Euclidean Representations for Solid Mechanics
| Title: | Learning Non-Euclidean Representations for Solid Mechanics |
|---|---|
| Authors: | Xiao, Mian |
| Publication Year: | 2025 |
| Collection: | Columbia University: Academic Commons |
| Subject Terms: | Civil engineering, Machine learning--Industrial applications, Artificial intelligence--Industrial applications, Anisotropy, Geometry, Non-Euclidean, Strains and stresses--Analysis |
| Description: | In the recent advancement of applying machine learning (ML) methods to solid mechanics modeling, ML models have made a great leap over conventional hand-crafted mechanical models in terms of model capacity and generalizability. However, these models could still fail to predict locally, especially in engineering extreme event cases, when material behaviors are significantly complicated by large deformations and high strain rates. Hence, geometric learning, a branch of ML, demonstrates a greater potential due to its ability to incorporate the non-Euclidean representations of the data obtained from mechanical solutions. This dissertation proposes a series of geometric-learning-assisted computational mechanics models covering both microscale constitutive modeling and macroscale structural modeling. The objective is to extract the non-Euclidean representations of mechanics problems’ solutions for building smart, powerful, and efficient solid mechanics models, which better suit the demanding model capacity required by extreme event engineering modeling.Firstly, the author demonstrates how to learn non-Euclidean representations for both microscale constitutive models and macroscale structural behaviors. In the case of microscale constitutive modeling, the yield surface is represented as a manifold reconstructed from multiple overlapping coordinate charts, each with a specific local parametrization. This approach enhances model generalizability by enabling adaptive resolution without overly complicating the parametrization. Additionally, a stress integration algorithm that projects trial stress directly onto local patches mitigates issues related to non-smoothness and convexity. In the case of macroscale structural modeling, a graph-manifold iterative algorithm is developed to predict the configurations of geometrically exact shells under external loading. Finite element solutions are embedded into a low-dimensional latent space through a graph isomorphism encoder, allowing the deformed configuration to be predicted ... |
| Document Type: | thesis |
| Language: | English |
| DOI: | 10.7916/37qe-6t56 |
| Availability: | https://doi.org/10.7916/37qe-6t56 |
| Accession Number: | edsbas.38102B9A |
| Database: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://doi.org/10.7916/37qe-6t56# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| Items | – Name: Title Label: Title Group: Ti Data: Learning Non-Euclidean Representations for Solid Mechanics – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Xiao%2C+Mian%22">Xiao, Mian</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2025 – Name: Subset Label: Collection Group: HoldingsInfo Data: Columbia University: Academic Commons – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Civil+engineering%22">Civil engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning--Industrial+applications%22">Machine learning--Industrial applications</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+intelligence--Industrial+applications%22">Artificial intelligence--Industrial applications</searchLink><br /><searchLink fieldCode="DE" term="%22Anisotropy%22">Anisotropy</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Non-Euclidean%22">Non-Euclidean</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+and+stresses--Analysis%22">Strains and stresses--Analysis</searchLink> – Name: Abstract Label: Description Group: Ab Data: In the recent advancement of applying machine learning (ML) methods to solid mechanics modeling, ML models have made a great leap over conventional hand-crafted mechanical models in terms of model capacity and generalizability. However, these models could still fail to predict locally, especially in engineering extreme event cases, when material behaviors are significantly complicated by large deformations and high strain rates. Hence, geometric learning, a branch of ML, demonstrates a greater potential due to its ability to incorporate the non-Euclidean representations of the data obtained from mechanical solutions. This dissertation proposes a series of geometric-learning-assisted computational mechanics models covering both microscale constitutive modeling and macroscale structural modeling. The objective is to extract the non-Euclidean representations of mechanics problems’ solutions for building smart, powerful, and efficient solid mechanics models, which better suit the demanding model capacity required by extreme event engineering modeling.Firstly, the author demonstrates how to learn non-Euclidean representations for both microscale constitutive models and macroscale structural behaviors. In the case of microscale constitutive modeling, the yield surface is represented as a manifold reconstructed from multiple overlapping coordinate charts, each with a specific local parametrization. This approach enhances model generalizability by enabling adaptive resolution without overly complicating the parametrization. Additionally, a stress integration algorithm that projects trial stress directly onto local patches mitigates issues related to non-smoothness and convexity. In the case of macroscale structural modeling, a graph-manifold iterative algorithm is developed to predict the configurations of geometrically exact shells under external loading. Finite element solutions are embedded into a low-dimensional latent space through a graph isomorphism encoder, allowing the deformed configuration to be predicted ... – Name: TypeDocument Label: Document Type Group: TypDoc Data: thesis – Name: Language Label: Language Group: Lang Data: English – Name: DOI Label: DOI Group: ID Data: 10.7916/37qe-6t56 – Name: URL Label: Availability Group: URL Data: https://doi.org/10.7916/37qe-6t56 – Name: AN Label: Accession Number Group: ID Data: edsbas.38102B9A |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.7916/37qe-6t56 Languages: – Text: English Subjects: – SubjectFull: Civil engineering Type: general – SubjectFull: Machine learning--Industrial applications Type: general – SubjectFull: Artificial intelligence--Industrial applications Type: general – SubjectFull: Anisotropy Type: general – SubjectFull: Geometry Type: general – SubjectFull: Non-Euclidean Type: general – SubjectFull: Strains and stresses--Analysis Type: general Titles: – TitleFull: Learning Non-Euclidean Representations for Solid Mechanics Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Xiao, Mian IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2025 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa |
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