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Documentation of SolidMechanicsEmbeddedFracture solver (#2617)
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CusiniM authored Sep 27, 2023
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2 changes: 2 additions & 0 deletions src/coreComponents/physicsSolvers/PhysicsSolvers.rst
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solidMechanics/docs/SolidMechanics

contact/docs/ContactMechanics

fluidFlow/docs/SinglePhaseFlow

fluidFlow/docs/CompositionalMultiphaseFlow
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.. _ContactMechanicsSolver:

#####################################
Contact Mechanics Solver
#####################################

Governing Equations
--------------------------

GEOS contact solvers solve the the balance of linear momentum within a fractured solid, accounting for the continuity of stress across surfaces (i.e., fractures), i.e.

.. math::
\nabla \cdot \sigma = 0 \\\\
[[\sigma]] \cdot \mathbf{n} = 0
Where:

* :math:`\sigma` is the stress tensor in the solid,
* :math:`\mathbf{n}` is the outward unit normal to the surface,
* :math:`[[\sigma]]` is the stress jump across the surface.

On each fracture surface, a no-interpenetration constraint is enforced. Additionally, tangential tractions can also be generated, which are modeled using a regularized Coulomb model to describe frictional sliding.

Solvers
--------------------------

There exist two broad classes of discretization methods that model fractures as lower dimensional entities
(eg, 2D surfaces in a 3D domain): conforming grid methods and nonconforming (or embedded) methods. Both approaches have
been implemented in GEOS in the following solvers:

.. toctree::
:maxdepth: 1

SolidMechanicsConformingFractures

SolidMechanicsEmbeddedFractures
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.. _SolidMechanicsConformingFractures:

#####################################
Solid mechanics conforming fractures solver
#####################################

Introduction
============


Theory
=========================

Under construction

Governing Equations
--------------------------

Under construction

Parameters
=========================

In the preceding XML block, The `LagrangianContactSolver` is specified by the title of the subblock of the `Solvers` block.
The following attributes are supported in the input block for `LagrangianContactSolver`:

.. include:: /coreComponents/schema/docs/LagrangianContactSolver.rst

The following data are allocated and used by the solver:

.. include:: /coreComponents/schema/docs/LagrangianContactSolver_other.rst

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.. _SolidMechanicsEmbeddedFractures:

#####################################
Solid mechanics embedded fractures solver
#####################################



Introduction
============


Discretization & soltuion strategy
=========================

The linear momentum balance equation is discretized using a low order finite element method. Moreover, to account for the influence of the fractures on the overall behavior, we utilize the enriched finite element method (EFEM)
with a piece-wise constant enrichment. This method employs an element-local enrichment of the FE space using the concept of assumedenhanced strain [1-6].


Example
=========================

An example of a valid XML block is given here:

.. literalinclude:: ../../../../../inputFiles/efemFractureMechanics/Sneddon_embeddedFrac_base.xml
:language: xml
:start-after: <!-- SPHINX_SNEDDON_SOLVER -->
:end-before: <!-- SPHINX_SNEDDON_SOLVER_END -->

Parameters
=========================

In the preceding XML block, The `SolidMechanicsEmbeddedFractures` is specified by the title of the subblock of the `Solvers` block.
Note that the `SolidMechanicsEmbeddedFractures` always relies on the existance of a
The following attributes are supported in the input block for `SolidMechanicsEmbeddedFractures`:

.. include:: /coreComponents/schema/docs/SolidMechanicsEmbeddedFractures.rst

The following data are allocated and used by the solver:

.. include:: /coreComponents/schema/docs/SolidMechanicsEmbeddedFractures_other.rst

References
==========

1. Simo JC, Rifai MS. A class of mixed assumed strain methods and the method of incompatible modes. *Int J Numer Methods Eng.* 1990;29(8):1595-1638. Available at: http://arxiv.org/abs/https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620290802.

2. Foster CD, Borja RI, Regueiro RA. Embedded strong discontinuity finite elements for fractured geomaterials with variable friction. *Int J Numer Methods Eng.* 2007;72(5):549-581. Available at: http://arxiv.org/abs/https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.2020.

3. Wells G, Sluys L. Three-dimensional embedded discontinuity model for brittle fracture. *Int J Solids Struct.* 2001;38(5):897-913. Available at: https://doi.org/10.1016/S0020-7683(00)00029-9.

4. Oliver J, Huespe AE, Sánchez PJ. A comparative study on finite elements for capturing strong discontinuities: E-fem vs x-fem. *Comput Methods Appl Mech Eng.* 2006;195(37-40):4732-4752. Available at: https://doi.org/10.1002/nme.4814.

5. Borja RI. Assumed enhanced strain and the extended finite element methods: a unification of concepts. *Comput Methods Appl Mech Eng.* 2008;197(33):2789-2803. Available at: https://doi.org/10.1016/j.cma.2008.01.019.

6. Wu J-Y. Unified analysis of enriched finite elements for modeling cohesive cracks. *Comput Methods Appl Mech Eng.* 2011;200(45-46):3031-3050. Available at: https://doi.org/10.1016/j.cma.2011.05.008.
9 changes: 8 additions & 1 deletion src/docs/sphinx/Publications.rst
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Publications
###############################################################################

Last updated 23-October-2022
Last updated 5-September-2023

Preprints and Early-Views
=========================

2023
====

* - | **A phase-field model for hydraulic fracture nucleation and propagation in porous media**
| F Fei, A Costa, JE Dolbow, R Settgast, M Cusini
| International Journal for Numerical and Analytical Methods in Geomechanics
| `doi.org/10.1002/nag.3612 <https://doi.org/10.1002/nag.3612>`_
2022
====
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2 changes: 2 additions & 0 deletions src/docs/sphinx/advancedExamples/validationStudies/Index.rst
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wellboreProblems/Index

viscoplasticity/Index

poromechanics/Index

thermoPoromechanics/Index

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.. _ValidationStudiesFaultMechanics:


Fault Mechanics
Faults & fractures
===================================

.. toctree::
:maxdepth: 1

sneddon/Example

singleFracCompression/Example

intersectFrac/Example

sneddon/Example

mandel/Example

faultVerification/Example
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.. _ValidationStudiesFaultMechanics:


Poromechanics
===================================

.. toctree::
:maxdepth: 1

mandel/Example

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