Work conjugate strain of virial stress
Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor. Virial stress is widely accepted as the stress measurement in molec...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2016-01-01
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| Series: | International Journal of Smart and Nano Materials |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/19475411.2016.1162218 |
| _version_ | 1831648660803289088 |
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| author | Leyu Wang Jiaoyan Li James D. Lee |
| author_facet | Leyu Wang Jiaoyan Li James D. Lee |
| author_sort | Leyu Wang |
| collection | DOAJ |
| description | Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor. Virial stress is widely accepted as the stress measurement in molecular dynamics (MD). However, its conjugate strain is not yet identified. An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at $$0\ {\rm{K}}$$ temperature. The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density. This conclusion is numerically verified with (1) Coulomb-Buckingham potential, Lenard-Jones potential, or arbitrary nonlinear pair potential and (2) randomly generated atomic configurations and deformation gradients. Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation. The result shows that the atomic logarithmic strain is identical to engineering strain when deformation is small. |
| first_indexed | 2024-12-19T14:35:35Z |
| format | Article |
| id | doaj.art-1f58640094b047999dcaeeabfc763ad1 |
| institution | Directory Open Access Journal |
| issn | 1947-5411 1947-542X |
| language | English |
| last_indexed | 2024-12-19T14:35:35Z |
| publishDate | 2016-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | International Journal of Smart and Nano Materials |
| spelling | doaj.art-1f58640094b047999dcaeeabfc763ad12022-12-21T20:17:16ZengTaylor & Francis GroupInternational Journal of Smart and Nano Materials1947-54111947-542X2016-01-0171395110.1080/19475411.2016.11622181162218Work conjugate strain of virial stressLeyu Wang0Jiaoyan Li1James D. Lee2Center for Collision Safety and Analysis, College of Science, George Mason UniversitySchool of Engineering, Brown UniversityThe George Washington UniversityCertain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor. Virial stress is widely accepted as the stress measurement in molecular dynamics (MD). However, its conjugate strain is not yet identified. An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at $$0\ {\rm{K}}$$ temperature. The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density. This conclusion is numerically verified with (1) Coulomb-Buckingham potential, Lenard-Jones potential, or arbitrary nonlinear pair potential and (2) randomly generated atomic configurations and deformation gradients. Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation. The result shows that the atomic logarithmic strain is identical to engineering strain when deformation is small.http://dx.doi.org/10.1080/19475411.2016.1162218Thermodynamic pairconjugacyvirial stressatomic logarithmic strainmolecular dynamicsinteratomic potentialstrain energymagnesium oxide |
| spellingShingle | Leyu Wang Jiaoyan Li James D. Lee Work conjugate strain of virial stress International Journal of Smart and Nano Materials Thermodynamic pair conjugacy virial stress atomic logarithmic strain molecular dynamics interatomic potential strain energy magnesium oxide |
| title | Work conjugate strain of virial stress |
| title_full | Work conjugate strain of virial stress |
| title_fullStr | Work conjugate strain of virial stress |
| title_full_unstemmed | Work conjugate strain of virial stress |
| title_short | Work conjugate strain of virial stress |
| title_sort | work conjugate strain of virial stress |
| topic | Thermodynamic pair conjugacy virial stress atomic logarithmic strain molecular dynamics interatomic potential strain energy magnesium oxide |
| url | http://dx.doi.org/10.1080/19475411.2016.1162218 |
| work_keys_str_mv | AT leyuwang workconjugatestrainofvirialstress AT jiaoyanli workconjugatestrainofvirialstress AT jamesdlee workconjugatestrainofvirialstress |