The Green tensor of Mindlin’s anisotropic first strain gradient elasticity Article Swipe
Giacomo Po
,
Nikhil Chandra Admal
,
Markus Lazar
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1186/s41313-019-0015-2
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1186/s41313-019-0015-2
We derive the Green tensor of Mindlin’s anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient elastic constants in the general case of triclinic media. In contrast to its classical counterpart, the Green tensor is non-singular at the origin, and it converges to the classical tensor a few characteristic lengths away from the origin. Therefore, the Green tensor of Mindlin’s first strain gradient elasticity can be regarded as a physical regularization of the classical anisotropic Green tensor. The isotropic Green tensor and other special cases are recovered as particular instances of the general anisotropic result. The Green tensor is implemented numerically and applied to the Kelvin problem with elastic constants determined from interatomic potentials. Results are compared to molecular statics calculations carried out with the same potentials.
Related Topics
Concepts
Strain rate tensor
Isotropy
Viscous stress tensor
Anisotropy
Tensor (intrinsic definition)
Elasticity (physics)
Hooke's law
Tensor field
Tensor density
Tensor contraction
Infinitesimal strain theory
Mathematical analysis
Cartesian tensor
Symmetric tensor
Cauchy stress tensor
Mathematics
Classical mechanics
Physics
Exact solutions in general relativity
Geometry
Thermodynamics
Quantum mechanics
Finite element method
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1186/s41313-019-0015-2
- https://materialstheory.springeropen.com/track/pdf/10.1186/s41313-019-0015-2
- OA Status
- gold
- Cited By
- 15
- References
- 33
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2916263707
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2916263707Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1186/s41313-019-0015-2Digital Object Identifier
- Title
-
The Green tensor of Mindlin’s anisotropic first strain gradient elasticityWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2019Year of publication
- Publication date
-
2019-03-15Full publication date if available
- Authors
-
Giacomo Po, Nikhil Chandra Admal, Markus LazarList of authors in order
- Landing page
-
https://doi.org/10.1186/s41313-019-0015-2Publisher landing page
- PDF URL
-
https://materialstheory.springeropen.com/track/pdf/10.1186/s41313-019-0015-2Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
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https://materialstheory.springeropen.com/track/pdf/10.1186/s41313-019-0015-2Direct OA link when available
- Concepts
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Strain rate tensor, Isotropy, Viscous stress tensor, Anisotropy, Tensor (intrinsic definition), Elasticity (physics), Hooke's law, Tensor field, Tensor density, Tensor contraction, Infinitesimal strain theory, Mathematical analysis, Cartesian tensor, Symmetric tensor, Cauchy stress tensor, Mathematics, Classical mechanics, Physics, Exact solutions in general relativity, Geometry, Thermodynamics, Quantum mechanics, Finite element methodTop concepts (fields/topics) attached by OpenAlex
- Cited by
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15Total citation count in OpenAlex
- Citations by year (recent)
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2025: 1, 2024: 4, 2023: 3, 2022: 3, 2021: 2Per-year citation counts (last 5 years)
- References (count)
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33Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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