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:

    <SolidMechanicsEmbeddedFractures
      name="mechSolve"
      targetRegions="{ Domain, Fracture }"
      initialDt="10"
      timeIntegrationOption="QuasiStatic"
      discretization="FE1"
      logLevel="1"
      contactPenaltyStiffness="0.0e8">
      <NonlinearSolverParameters
        newtonTol="1.0e-6"
        newtonMaxIter="2"
        maxTimeStepCuts="1"/>
      <LinearSolverParameters
        solverType="direct"
        directParallel="0"
        logLevel="0"/>
    </SolidMechanicsEmbeddedFractures>

    <EmbeddedSurfaceGenerator
      name="SurfaceGenerator"
      discretization="FE1"
      targetRegions="{ Domain, Fracture }"
      fractureRegion="Fracture"
      targetObjects="{ FracturePlane }"
      logLevel="1"
      mpiCommOrder="1"/>
  </Solvers>

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:

XML Element: 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]
contactPenaltyStiffness	real64	required	Value of the penetration penalty stiffness. Units of Pressure/length
discretization	groupNameRef	required	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.
initialDt	real64	1e+99	Initial time-step value required by the solver to the event manager.
logLevel	integer	0	Sets the level of information to write in the standard output (the console typically). Level 0 outputs no specific information for this solver. Higher levels require more outputs. 1 - Line search information - Solution information (scaling, maximum changes, quality check) - Convergence information - Time step information - Linear solver information - Nonlinear solver information - Solver timers information 2 - The summary of declared fields and coupling
massDamping	real64	0	Value of mass based damping coefficient.
maxNumResolves	integer	10	Value to indicate how many resolves may be executed after some other event is executed. For example, if a SurfaceGenerator is specified, it will be executed after the mechanics solve. However if a new surface is generated, then the mechanics solve must be executed again due to the change in topology.
name	groupName	required	A name is required for any non-unique nodes
newmarkBeta	real64	0.25	Value of $\beta$ in the Newmark Method for Implicit Dynamic time integration option. This should be pow(newmarkGamma+0.5,2.0)/4.0 unless you know what you are doing.
newmarkGamma	real64	0.5	Value of $\gamma$ in the Newmark Method for Implicit Dynamic time integration option
stiffnessDamping	real64	0	Value of stiffness based damping coefficient.
strainTheory	integer	0	Indicates whether or not to use Infinitesimal Strain Theory, or Finite Strain Theory. Valid Inputs are: 0 - Infinitesimal Strain 1 - Finite Strain
targetRegions	groupNameRef_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.
timeIntegrationOption	geos_SolidMechanicsLagrangianFEM_TimeIntegrationOption	ExplicitDynamic	Time integration method. Options are: * QuasiStatic * ImplicitDynamic * ExplicitDynamic
useStaticCondensation	integer	0	Defines whether to use static condensation or not.
writeLinearSystem	integer	0	Write matrix, rhs, solution to screen ( = 1) or file ( = 2).
LinearSolverParameters	node	unique	XML Element: LinearSolverParameters
NonlinearSolverParameters	node	unique	XML Element: NonlinearSolverParameters

The following data are allocated and used by the solver:

Datastructure: SolidMechanicsEmbeddedFractures

Name	Type	Description
contactRelationName	groupNameRef	Name of contact relation to enforce constraints on fracture boundary.
maxForce	real64	The maximum force contribution in the problem domain.
maxStableDt	real64	Value of the Maximum Stable Timestep for this solver.
meshTargets	geos_mapBase<std___1_pair<std___1_basic_string<char, std___1_char_traits<char>, std___1_allocator<char>>, std___1_basic_string<char, std___1_char_traits<char>, std___1_allocator<char>>>, LvArray_Array<std___1_basic_string<char, std___1_char_traits<char>, std___1_allocator<char>>, 1, camp_int_seq<long, 0l>, int, LvArray_ChaiBuffer>, std___1_integral_constant<bool, true>>	MeshBody/Region combinations that the solver will be applied to.
surfaceGeneratorName	string	Name of the surface generator to use
LinearSolverParameters	node	Datastructure: LinearSolverParameters
NonlinearSolverParameters	node	Datastructure: NonlinearSolverParameters
SolverStatistics	node	Datastructure: SolverStatistics

References

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.
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.
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.
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.
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.
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.