Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon
Abstract
Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.
- Publication Date:
- Research Org.:
- Ames Laboratory (AMES), Ames, IA (United States); Iowa State Univ., Ames, IA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); National Key Research and Development Program of China; National Natural Science Foundation of China (NSFC)
- OSTI Identifier:
- 1644704
- Alternate Identifier(s):
- OSTI ID: 1645120
- Report Number(s):
- IS-J-10,239
Journal ID: ISSN 2057-3960; 115; PII: 382
- Grant/Contract Number:
- AC02-07CH11358; N00014-16-1-2079
- Resource Type:
- Published Article
- Journal Name:
- npj Computational Materials
- Additional Journal Information:
- Journal Name: npj Computational Materials Journal Volume: 6 Journal Issue: 1; Journal ID: ISSN 2057-3960
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; Atomistic models; Mechanical properties
Citation Formats
Chen, Hao, Zarkevich, Nikolai A., Levitas, Valery I., Johnson, Duane D., and Zhang, Xiancheng. Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon. United Kingdom: N. p., 2020.
Web. doi:10.1038/s41524-020-00382-8.
Chen, Hao, Zarkevich, Nikolai A., Levitas, Valery I., Johnson, Duane D., & Zhang, Xiancheng. Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon. United Kingdom. https://doi.org/10.1038/s41524-020-00382-8
Chen, Hao, Zarkevich, Nikolai A., Levitas, Valery I., Johnson, Duane D., and Zhang, Xiancheng. Tue .
"Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon". United Kingdom. https://doi.org/10.1038/s41524-020-00382-8.
@article{osti_1644704,
title = {Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon},
author = {Chen, Hao and Zarkevich, Nikolai A. and Levitas, Valery I. and Johnson, Duane D. and Zhang, Xiancheng},
abstractNote = {Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.},
doi = {10.1038/s41524-020-00382-8},
journal = {npj Computational Materials},
number = 1,
volume = 6,
place = {United Kingdom},
year = {Tue Aug 04 00:00:00 EDT 2020},
month = {Tue Aug 04 00:00:00 EDT 2020}
}
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