Articles | Volume 12, issue 4
https://doi.org/10.5194/se-12-817-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-12-817-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
15 Apr 2021
Research article |
| 15 Apr 2021
| 15 Apr 2021
Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host
Xin Zhong
CORRESPONDING AUTHOR
Institut für Geologische Wissenschaften, Freie Universität Berlin,
Malteserstrasse 74–100, 12449 Berlin, Germany
Physics of Geological Processes, The Njord Center, University of Oslo, Oslo,
Norway
Marcin Dabrowski
Physics of Geological Processes, The Njord Center, University of Oslo, Oslo,
Norway
Computational Geology Laboratory, Polish Geological Institute – NRI,
Wrocław, Poland
Bjørn Jamtveit
Physics of Geological Processes, The Njord Center, University of Oslo, Oslo,
Norway
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Cited
19 citations as recorded by crossref.
- Thermal expansivity and Raman spectra of natural cordierite: A potential cordierite-garnet elastic thermometer Y. Hu et al. https://doi.org/10.1016/j.pepi.2022.106939
- Quartz under stress: Raman calibration and applications of metamorphic inclusions to geobarometry B. Reynard & X. Zhong https://doi.org/10.5194/se-14-591-2023
- Re-equilibration of quartz inclusions in garnet B. Pummell & J. Thomas https://doi.org/10.5194/ejm-36-581-2024
- Equation of state of spinel (MgAl2O4): constraints on self-consistent thermodynamic parameters and implications for elastic geobarometry of peridotites and chromitites Y. Hagiwara et al. https://doi.org/10.1007/s00410-022-01975-w
- The effect of aqueous fluid on viscous relaxation of garnet and modification of inclusion pressures after entrapment X. Zhong et al. https://doi.org/10.1016/j.epsl.2024.118713
- Combined phase diagram modelling and quartz‐in‐garnet barometry of HP metapelites from the Kamieniec Metamorphic Belt (NE Bohemian Massif) J. Szczepański et al. https://doi.org/10.1111/jmg.12608
- High P-T single-crystal elasticity of zircon by Brillouin spectroscopy A. Luu et al. https://doi.org/10.2138/am-2024-9458
- Elasticity of mixtures and implications for piezobarometry of mixed-phase inclusions R. Angel et al. https://doi.org/10.5194/ejm-35-461-2023
- Large-strain Elastic and Elasto-Plastic Formulations for Host-Inclusion Systems and Their Applications in Thermobarometry and Geodynamics E. Moulas et al. https://doi.org/10.2475/001c.68195
- A brief history of solid inclusion piezobarometry R. Angel et al. https://doi.org/10.5194/ejm-36-411-2024
- Ultrahigh-temperature metamorphism revealed by felsic granulite xenoliths in southern Tibet W. Sun et al. https://doi.org/10.1130/B37694.1
- Investigation of microscale brittle fracture opening in diamond with olivine inclusion using XFEM and cohesive zone modeling B. Puhan et al. https://doi.org/10.1016/j.engfracmech.2024.110713
- A re-evaluation of prograde pressure-temperature paths of eclogites from the Tongbai orogen by quartz-in-garnet and Ti-in-calcic amphibole thermobarometry Y. Wang et al. https://doi.org/10.1007/s00410-025-02265-x
- Mafic-Ultramafic Subduction Complexes of the Belomorian Eclogite Province: Composition and Formation Conditions K. Dokukina et al. https://doi.org/10.24930/2500-302X-2026-26-3-540-564
- Stressful crystal histories recorded around melt inclusions in volcanic quartz T. Cadena et al. https://doi.org/10.1007/s00410-024-02126-z
- Lower crustal earthquake associated with highly pressurized frictional melts X. Zhong et al. https://doi.org/10.1038/s41561-021-00760-x
- Elastic Thermobarometry M. Kohn et al. https://doi.org/10.1146/annurev-earth-031621-112720
- Modeling diffusion in ionic, crystalline solids with internal stress gradients B. Hess & J. Ague https://doi.org/10.1016/j.gca.2023.06.004
- Equivalent Inclusion Method (EIM) for isotropic and anisotropic spatially oriented spheroidal inhomogeneities: A unified calculation module validated via comparisons to Finite Element (FE) simulations R. Serre et al. https://doi.org/10.1016/j.mechmat.2024.105194
19 citations as recorded by crossref.
- Thermal expansivity and Raman spectra of natural cordierite: A potential cordierite-garnet elastic thermometer Y. Hu et al. https://doi.org/10.1016/j.pepi.2022.106939
- Quartz under stress: Raman calibration and applications of metamorphic inclusions to geobarometry B. Reynard & X. Zhong https://doi.org/10.5194/se-14-591-2023
- Re-equilibration of quartz inclusions in garnet B. Pummell & J. Thomas https://doi.org/10.5194/ejm-36-581-2024
- Equation of state of spinel (MgAl2O4): constraints on self-consistent thermodynamic parameters and implications for elastic geobarometry of peridotites and chromitites Y. Hagiwara et al. https://doi.org/10.1007/s00410-022-01975-w
- The effect of aqueous fluid on viscous relaxation of garnet and modification of inclusion pressures after entrapment X. Zhong et al. https://doi.org/10.1016/j.epsl.2024.118713
- Combined phase diagram modelling and quartz‐in‐garnet barometry of HP metapelites from the Kamieniec Metamorphic Belt (NE Bohemian Massif) J. Szczepański et al. https://doi.org/10.1111/jmg.12608
- High P-T single-crystal elasticity of zircon by Brillouin spectroscopy A. Luu et al. https://doi.org/10.2138/am-2024-9458
- Elasticity of mixtures and implications for piezobarometry of mixed-phase inclusions R. Angel et al. https://doi.org/10.5194/ejm-35-461-2023
- Large-strain Elastic and Elasto-Plastic Formulations for Host-Inclusion Systems and Their Applications in Thermobarometry and Geodynamics E. Moulas et al. https://doi.org/10.2475/001c.68195
- A brief history of solid inclusion piezobarometry R. Angel et al. https://doi.org/10.5194/ejm-36-411-2024
- Ultrahigh-temperature metamorphism revealed by felsic granulite xenoliths in southern Tibet W. Sun et al. https://doi.org/10.1130/B37694.1
- Investigation of microscale brittle fracture opening in diamond with olivine inclusion using XFEM and cohesive zone modeling B. Puhan et al. https://doi.org/10.1016/j.engfracmech.2024.110713
- A re-evaluation of prograde pressure-temperature paths of eclogites from the Tongbai orogen by quartz-in-garnet and Ti-in-calcic amphibole thermobarometry Y. Wang et al. https://doi.org/10.1007/s00410-025-02265-x
- Mafic-Ultramafic Subduction Complexes of the Belomorian Eclogite Province: Composition and Formation Conditions K. Dokukina et al. https://doi.org/10.24930/2500-302X-2026-26-3-540-564
- Stressful crystal histories recorded around melt inclusions in volcanic quartz T. Cadena et al. https://doi.org/10.1007/s00410-024-02126-z
- Lower crustal earthquake associated with highly pressurized frictional melts X. Zhong et al. https://doi.org/10.1038/s41561-021-00760-x
- Elastic Thermobarometry M. Kohn et al. https://doi.org/10.1146/annurev-earth-031621-112720
- Modeling diffusion in ionic, crystalline solids with internal stress gradients B. Hess & J. Ague https://doi.org/10.1016/j.gca.2023.06.004
- Equivalent Inclusion Method (EIM) for isotropic and anisotropic spatially oriented spheroidal inhomogeneities: A unified calculation module validated via comparisons to Finite Element (FE) simulations R. Serre et al. https://doi.org/10.1016/j.mechmat.2024.105194
Saved (final revised paper)
Latest update: 24 Aug 2026
Short summary
Elastic thermobarometry is an useful tool to recover paleo-pressure and temperature. Here, we provide an analytical model based on the Eshelby solution to calculate the residual stress and strain preserved in a mineral inclusion exhumed from depth. The method applies to ellipsoidal, anisotropic inclusions in infinite isotropic hosts. A finite-element method is also used for a facet effect. Volumetrically averaged stress is shown to be a good proxy for the overall heterogeneous stress stage.
Elastic thermobarometry is an useful tool to recover paleo-pressure and temperature. Here, we...
