Esh3D, an analytical-numerical hybrid code for interactive Eshelby's inclusion problems in whole, half and finite spaces

Corresponding author: Chunfang Meng ( cmeng (at) mit.edu )
Contributors: Pradeep Sharma ( psharma (at) uh.edu ), Will Heltsley and Tabrez Ali ( tabrez.ali (at) gmail.com )

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DESCRIPTION

This is a Fortran translation and extension of the Matlab code (Meng et al, 2011) for triaxial Eshebly's solution evaluation. Numerical part of the code is derived from Defmod and Defmod-SWPC.

This code, as an improvement over the original,

• runs much quicker;
• allows arbitrary number of arbitrarily oriented Eshelby's inclusions;
• (optionally) applies numerical traction cancellation to obtain topographical half space Eshelby solution;
• includes a custom (Okada, 1992) subroutine allowing joint Eshelby + Okada models;
• evaluates Okada solution for topographical surface.

Eshelby vs Okada

• Eshelby model, with six-component eigen strain tensors, considers volumetric inclsion transformations.
• The semi-numerical-analytical approach to half space solution allows non-planar surface.
• Slightly more expensive if the numerical (FEM) half space correction is engaged.

INSTALL

• 3rd party package PETSc built with HDF5, e.g. configured with --download-hdf5.
• At src folder, run make all to build.
• To obtain half space solution, Trelis/Cubit mesh (hex or tet) is expected by preprocessor (python) script.

RUN

Analytical (full space) solution

• At example folder edit esh3d.py file "half=False", and run ./esh3d.py to generate esh3d.inp;
• run ../bin/esh3d -f esh3d.inp

Semi-analytical-numerical (half space) solution

• Run trelis[cubit] -nojournal -nographics esh3d.jou to generate FE mesh esh3d.exo.
• Have "half=True" in esh3d.py, and run ./esh3d esh3d.exo to produce esh3d.inp with the mesh.
• run mpirun ../bin/esh3d -f esh3d.inp

Use the Python and Cubit scripts as templates to roll custom models.

Result visualization

A HDF5 file can be imported to Matlab, Python and Hdfview

• ellip, inclusion parameters, see esh3d.py for explanation;
• ocoord, evaluation locations (x,y,z km);
• odat, evaluation data, column 1-3 displacement (ux,uy,yz m); column 4-9 stress (s11,s22,s33,s12,s23,s13 Pa);

Additionally, if the "half" option is on

• scoord, surface element centroid locations;
• sdat, displacement and stress at surface element centroids for full and half space (9+9 columns).

Note, the full space solution is stored even if the "half" option is on.

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LICENSE

MIT License, see LICENSE for details.

The authors appreciate that the users cite the following papers in any publications employing this code. For feedback or contribution, please contact the corresponding author.

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REFERENCES

• Meng, C., W. Heltsley, and D. Pollard, 2012, "Evaluation of the Eshelby Solution for the Ellipsoidal Inclusion and Heterogeneity", Computers & Geosciences, Vols. 40, pp. 40 - 48, https://doi.org/10.1016/j.cageo.2011.07.008.
• Meng, C., F. Maerten, D. Pollard, 2012. “Modeling mixed-mode fracture propagation in isotropic elastic three dimensional solid”, International Journal of Fracture, Vols. 179, pp. 45– 57, https://doi.org/10.1007/s10704-012-9771-6.
• Meng, C., D. Pollard, 2014, “Eshelby’s solution for ellipsoidal inhomogeneous inclusions with applications to compaction bands”, Journal of Structural Geology, Vols. 67, pp. 1 - 19, https://doi.org/10.1016/j.jsg.2014.07.002.
• Ali, T., Defmod - Parallel multiphysics finite element code for modeling crustal deformation during the earthquake/rifting cycle, https://arxiv.org/abs/1402.0429.
• Meng, C., 2019, “Esh3D. an analytical and numerical hybrid code for full and half space Eshelby's inclusion problems”, Earth and Space Science, https://doi.org/10.1029/2018EA000442.
• Meng, C., 2019, “Extneding Esh3D code to solve interactive Eshelby's inhomogeneity problems”, Earth and Space Science, https://doi.org/10.1029/2019EA000594.