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A numerical application of the Eshelby theory for geobarometry of non-ideal host-inclusion systems

  • Computational Models for ’Complex’ Materials and Structures, beyond the Finite Elements
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Abstract

In the complex geodynamic processes occurring at convergent plate margins, rocks can be subducted at depth into the Earth experiencing metamorphism. A mineral inhomogeneity entrapped into another mineral, after exhumation to the Earth surface, will exhibit stress and strain fields different from those of the host because of the different thermoelastic properties. In the present paper, we propose a finite-element-based approach to determine the Eshelby and the relaxations tensors for any morphology of the inhomogeneity and for any crystallographic symmetry of the host. The proposed procedure can be directly applied in the framework of elastic geobarometry to estimate, on the basis of the Eshelby theory, the entrapment conditions (pressure and temperature) from the residual strain field measured in the inhomogeneity. This aspect represents a step forward to currently available models for geobarometry allowing the investigation of complex morphologies of the inhomogeneity in systems with general material anisotropy. We validate the proposed approach versus Eshelby analytical solutions available for spherical and ellipsoidal inclusions and we show the application to a real geological case of high pressure metamorphic rocks.

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The figure is adapted from Anzolini et al. [9]

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Notes

  1. Material properties from Özkan et al. [33]

  2. Material properties from Angel et al. [4] and Lakshtanov et al. [24]

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Acknowledgements

AR has been partially supported by the MIUR-PRIN project XFAST-SIMS (No. 20173C478N) while MA and MLM have been partially supported by the the ERC-StG 2016 TRUE DEPTHS (Grant 714936) and by the FARE-MIUR: StackIng disorder in diaMonds as a marker for the history of Pre-solAr Carbon (IMPACt, FARE-MIUR n. R164WEJAHH).

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Authors and Affiliations

  1. Department of Electrical, Computer, and Biomedical Engineering, University of Pavia, Pavia, Italy

    S. Morganti

  2. Department of Earth and Environmental Sciences, University of Pavia, Pavia, Italy

    M. L. Mazzucchelli & M. Alvaro

  3. Department of Civil Engineering and Architecture, University of Pavia, Pavia, Italy

    A. Reali

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  1. S. Morganti
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  2. M. L. Mazzucchelli
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  3. M. Alvaro
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  4. A. Reali
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Correspondence to A. Reali.

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Appendix: Eshelby and relaxation tensors

Appendix: Eshelby and relaxation tensors

We here report the components of \(\varvec{S}\) and \(\varvec{R}\) computed both with an analytical approach and with a finite element-based numerical methodology for the case of an ellipsoidal quartz inhomogeneity in zircon host (see Sect. 5.1). Elastic isotropic constitutive equations are assumed for both the minerals. The considered model is discretized with \(\approx 3 \cdot 10^5\) nodes.

Table 1 Components of the Eshelby tensor (\(\varvec{S}\)) calculated with the numerical approach proposed in this paper and compared against the analytical solution
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Table 2 Components of the relaxation tensor (\(\varvec{R}\)) calculated with the numerical approach proposed in this paper and compared against the analytical solution
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Morganti, S., Mazzucchelli, M.L., Alvaro, M. et al. A numerical application of the Eshelby theory for geobarometry of non-ideal host-inclusion systems. Meccanica 55, 751–764 (2020). https://doi.org/10.1007/s11012-020-01135-z

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