Fully implicit crystal plasticity models representing orientations with modified Rodrigues parameters.
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| Title: | Fully implicit crystal plasticity models representing orientations with modified Rodrigues parameters. |
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| Authors: | Messner, Mark C.1 (AUTHOR) messner@anl.gov, Hu, Tianchen1 (AUTHOR) |
| Source: | Mechanics of Materials. Sep2025, Vol. 208, pN.PAG-N.PAG. 1p. |
| Subjects: | Time integration scheme, Mathematical formulas, Crystal models, Crystal orientation, Single crystals |
| Abstract: | This work describes a crystal plasticity formulation combining several mathematical, numerical, and implementation choices to produce a highly efficient model. Specifically, the key choices in the implementation are (1) representing orientations with modified Rodrigues parameters, (2) implementing a fully coupled implicit time integration for the elastic stretch, the crystal orientations, and the model internal variables, (3) implementing the model in the NEML2 constitutive modeling framework, based on PyTorch, to vectorize the calculations and port the computation to GPUs and other hardware accelerators, and (4) an exact implementation of the consistent tangent matrix, even for arbitrary coupling to other field variables beyond the displacements, like temperature, neutron fluence, etc. The first two features of the model are, to our knowledge, novel. The paper considers each of these choices individually as well as the final model as a whole. This includes a full description of modified Rodrigues parameters, their advantages over other representations of orientations, the mathematical formulae and tools required to implement a model with modified Rodrigues parameters, and a detailed description of the geometry of the space of modified Rodrigues parameters (in an appendix). It also includes a description of a fully implicit time integration scheme for the orientations and the advantages in representing orientations with modified Rodrigues parameters in implementing such a model. The work then assess, via numerical examples, the advantages of fully coupled implicit time integration versus more common decoupled and explicit time integration schemes. These studies demonstrate the computational advantages of fully coupled integration versus other time integration algorithms, though the performance of the competing models depends on the complexity of the underlying single crystal model. The study concludes by demonstrating that the choice of time integration method affects the sharpness of the predicted texture, with explicit methods for integrating the orientations overestimating texture sharpness and implicit methods underestimating texture sharpness. • Describes a highly efficient crystal plasticity formulation and implementation. • Compares implicit, semi-implicit, and explict integration strategies for rotations. • Demonstrates a difference in the sharpness of textures across integration techniques. • Details advantages of representing orientations with modified Rodrigues parameters. • Describes the geometry of modified Rodrigues space. [ABSTRACT FROM AUTHOR] |
| Copyright of Mechanics of Materials is the property of Elsevier B.V. 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: 186642358 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Fully implicit crystal plasticity models representing orientations with modified Rodrigues parameters. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Messner%2C+Mark+C%2E%22">Messner, Mark C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> messner@anl.gov</i><br /><searchLink fieldCode="AR" term="%22Hu%2C+Tianchen%22">Hu, Tianchen</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mechanics+of+Materials%22">Mechanics of Materials</searchLink>. Sep2025, Vol. 208, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Time+integration+scheme%22">Time integration scheme</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+formulas%22">Mathematical formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Crystal+models%22">Crystal models</searchLink><br /><searchLink fieldCode="DE" term="%22Crystal+orientation%22">Crystal orientation</searchLink><br /><searchLink fieldCode="DE" term="%22Single+crystals%22">Single crystals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This work describes a crystal plasticity formulation combining several mathematical, numerical, and implementation choices to produce a highly efficient model. Specifically, the key choices in the implementation are (1) representing orientations with modified Rodrigues parameters, (2) implementing a fully coupled implicit time integration for the elastic stretch, the crystal orientations, and the model internal variables, (3) implementing the model in the NEML2 constitutive modeling framework, based on PyTorch, to vectorize the calculations and port the computation to GPUs and other hardware accelerators, and (4) an exact implementation of the consistent tangent matrix, even for arbitrary coupling to other field variables beyond the displacements, like temperature, neutron fluence, etc. The first two features of the model are, to our knowledge, novel. The paper considers each of these choices individually as well as the final model as a whole. This includes a full description of modified Rodrigues parameters, their advantages over other representations of orientations, the mathematical formulae and tools required to implement a model with modified Rodrigues parameters, and a detailed description of the geometry of the space of modified Rodrigues parameters (in an appendix). It also includes a description of a fully implicit time integration scheme for the orientations and the advantages in representing orientations with modified Rodrigues parameters in implementing such a model. The work then assess, via numerical examples, the advantages of fully coupled implicit time integration versus more common decoupled and explicit time integration schemes. These studies demonstrate the computational advantages of fully coupled integration versus other time integration algorithms, though the performance of the competing models depends on the complexity of the underlying single crystal model. The study concludes by demonstrating that the choice of time integration method affects the sharpness of the predicted texture, with explicit methods for integrating the orientations overestimating texture sharpness and implicit methods underestimating texture sharpness. • Describes a highly efficient crystal plasticity formulation and implementation. • Compares implicit, semi-implicit, and explict integration strategies for rotations. • Demonstrates a difference in the sharpness of textures across integration techniques. • Details advantages of representing orientations with modified Rodrigues parameters. • Describes the geometry of modified Rodrigues space. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mechanics of Materials is the property of Elsevier B.V. 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.mechmat.2025.105388 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Time integration scheme Type: general – SubjectFull: Mathematical formulas Type: general – SubjectFull: Crystal models Type: general – SubjectFull: Crystal orientation Type: general – SubjectFull: Single crystals Type: general Titles: – TitleFull: Fully implicit crystal plasticity models representing orientations with modified Rodrigues parameters. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Messner, Mark C. – PersonEntity: Name: NameFull: Hu, Tianchen IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 01676636 Numbering: – Type: volume Value: 208 Titles: – TitleFull: Mechanics of Materials Type: main |
| ResultId | 1 |
