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Title: Finite Strain Analysis of Shear and Compressional Wave Velocities

Abstract

Published shear-modulus measurements for a wide variety of materials (Ar, Xe, H2, He, NaCl, H2O-VII, MgO, stishovite, bridgmanite) show that the Eulerian (spatial) description of energy vs. strain fits both finite- and infinitesimal-strain (e.g., wave velocity) elasticity data under high pressure. The Eulerian (spatial) formulations do so better than the Lagrangian (material) finite-strain description, with differences of 1% to 60% in both P- and S -wave velocities for these materials at the pressures of Earth's mantle. The findings are significant in extending to shear previous findings that compressional (pressure-volume and bulk-modulus) measurements are also best fit using the spatial formulation. Our assessment empirically documents that a self-consistent Eulerian finite-strain equation of state offers a reliable means of describing the thermodynamic and elastic properties of planetary interiors.

Authors:
ORCiD logo [1]; ORCiD logo [1]
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  1. Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1633877
Alternate Identifier(s):
OSTI ID: 1580618
Grant/Contract Number:  
NA0003842
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Geophysical Research. Solid Earth
Additional Journal Information:
Journal Volume: 124; Journal Issue: 11; Journal ID: ISSN 2169-9313
Publisher:
American Geophysical Union
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES

Citation Formats

Melinger‐Cohen, Ariel, and Jeanloz, Raymond. Finite Strain Analysis of Shear and Compressional Wave Velocities. United States: N. p., 2019. Web. doi:10.1029/2019JB017868.
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Melinger‐Cohen, Ariel, & Jeanloz, Raymond. Finite Strain Analysis of Shear and Compressional Wave Velocities. United States. https://doi.org/10.1029/2019JB017868
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Melinger‐Cohen, Ariel, and Jeanloz, Raymond. Thu . "Finite Strain Analysis of Shear and Compressional Wave Velocities". United States. https://doi.org/10.1029/2019JB017868. https://www.osti.gov/servlets/purl/1633877.
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@article{osti_1633877,
title = {Finite Strain Analysis of Shear and Compressional Wave Velocities},
author = {Melinger‐Cohen, Ariel and Jeanloz, Raymond},
abstractNote = {Published shear-modulus measurements for a wide variety of materials (Ar, Xe, H2, He, NaCl, H2O-VII, MgO, stishovite, bridgmanite) show that the Eulerian (spatial) description of energy vs. strain fits both finite- and infinitesimal-strain (e.g., wave velocity) elasticity data under high pressure. The Eulerian (spatial) formulations do so better than the Lagrangian (material) finite-strain description, with differences of 1% to 60% in both P- and S -wave velocities for these materials at the pressures of Earth's mantle. The findings are significant in extending to shear previous findings that compressional (pressure-volume and bulk-modulus) measurements are also best fit using the spatial formulation. Our assessment empirically documents that a self-consistent Eulerian finite-strain equation of state offers a reliable means of describing the thermodynamic and elastic properties of planetary interiors.},
doi = {10.1029/2019JB017868},
journal = {Journal of Geophysical Research. Solid Earth},
number = 11,
volume = 124,
place = {United States},
year = {2019},
month = {10}
}
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https://doi.org/10.1029/2019JB017868
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Cited by: 3 works
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Figures / Tables:

Figure 1 Figure 1: Schematic illustration of both infinitesimal and finite deformation of a material. (1) The original coordinates $a_i$ of the material. (2) The material in its intermediate state $X_i$ involving only volume compression. (3) The material in its final state $x_i$. Both $X_i$ and $x_i$ are deformed finitely from $a_i$,more » and infinitesimally from each other.« less
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