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:

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:

Name

Type

Default

Description

cflFactor

real64

0.5

Factor to apply to the CFL condition when calculating the maximum allowable time step. Values should be in the interval (0,1]

contactRelationName

string

required

Name of contact relation to enforce constraints on fracture boundary.

fractureRegionName

string

required

Name of the fracture region.

initialDt

real64

1e+99

Initial time-step value required by the solver to the event manager.

logLevel

integer

0

Log level

name

string

required

A name is required for any non-unique nodes

solidSolverName

string

required

Name of the solid mechanics solver in the rock matrix

targetRegions

string_array

required

Allowable regions that the solver may be applied to. Note that this does not indicate that the solver will be applied to these regions, only that allocation will occur such that the solver may be applied to these regions. The decision about what regions this solver will beapplied to rests in the EventManager.

useStaticCondensation

integer

0

Defines whether to use static condensation or not.

LinearSolverParameters

node

unique

Element: LinearSolverParameters

NonlinearSolverParameters

node

unique

Element: NonlinearSolverParameters

The following data are allocated and used by the solver:

Name

Type

Description

discretization

string

Name of discretization object (defined in the Numerical Methods) to use for this solver. For instance, if this is a Finite Element Solver, the name of a Finite Element Discretization should be specified. If this is a Finite Volume Method, the name of a Finite Volume Discretization discretization should be specified.

maxStableDt

real64

Value of the Maximum Stable Timestep for this solver.

meshTargets

geos_mapBase< std_pair< string, string >, LvArray_Array< string, 1, camp_int_seq< long, 0l >, int, LvArray_ChaiBuffer >, std_integral_constant< bool, true > >

MeshBody/Region combinations that the solver will be applied to.

LinearSolverParameters

node

Datastructure: LinearSolverParameters

NonlinearSolverParameters

node

Datastructure: NonlinearSolverParameters

SolverStatistics

node

Datastructure: SolverStatistics

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.