Fracture Mechanics Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Fracture Mechanics Ontology within the Kireth Research Semantic Library. Fracture mechanics studies the initiation, growth and instability of cracks and crack-like defects in solids and structures. This ontology supports stress intensity factors, energy release rate, fracture toughness, crack modes, linear elastic fracture mechanics, elastic-plastic fracture mechanics, J-integral, crack-tip fields, fatigue crack growth, Paris law, mixed-mode fracture, cohesive-zone modelling, crack closure, residual stress effects, instability criteria and relationships with stress analysis, strain analysis, elasticity, plasticity, structural analysis, materials science and finite element methods.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Fracture Mechanics Ontology"
 FLOW_TYPE = "Engineering Mathematics Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Engineering Mathematics / Fracture Mechanics"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/engineering-mathematics/fracture-mechanics-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = FractureMechanics
 SYMBOLIC_FORMS = [
  "K_I = Y*sigma*sqrt(pi*a)",
  "G = -dPi/dA",
  "J = integral_Gamma (W dy - T_i * partial u_i/partial x ds)"
 ]
 ENTITY_CLASS = CrackInitiationGrowthAndFailureFramework
 PRIMARY_CONTEXT = EngineeringMathematics
 DEFINITION = "Fracture mechanics is the mathematical study of crack-tip fields, crack initiation, crack growth and structural instability caused by flaws or discontinuities."
 SEMANTIC_ROLE = "Provides machine-readable semantics for stress intensity, fracture toughness, energy release, J-integral, crack growth, mixed-mode loading, fatigue fracture and crack-tip numerical analysis."
}

SCOPE {
 INCLUDE = [
  FractureMechanics,
  Crack,
  CrackTip,
  CrackFront,
  CrackLength,
  CrackSurface,
  CrackGrowth,
  CrackInitiation,
  CrackPropagation,
  StableCrackGrowth,
  UnstableFracture,
  BrittleFracture,
  DuctileFracture,
  LinearElasticFractureMechanics,
  LEFM,
  ElasticPlasticFractureMechanics,
  EPFM,
  ModeI,
  ModeII,
  ModeIII,
  MixedModeFracture,
  StressIntensityFactor,
  K_I,
  K_II,
  K_III,
  FractureToughness,
  CriticalStressIntensity,
  K_IC,
  EnergyReleaseRate,
  CriticalEnergyReleaseRate,
  GriffithCriterion,
  JIntegral,
  CriticalJIntegral,
  J_IC,
  CTOD,
  CrackTipOpeningDisplacement,
  ProcessZone,
  PlasticZone,
  SmallScaleYielding,
  PlaneStressFracture,
  PlaneStrainFracture,
  CrackTipSingularity,
  WilliamsExpansion,
  TStress,
  FatigueCrackGrowth,
  StressIntensityRange,
  DeltaK,
  ParisLaw,
  ThresholdStressIntensityRange,
  CrackClosure,
  RRatio,
  ResidualStress,
  EnvironmentalFracture,
  StressCorrosionCracking,
  CohesiveZoneModel,
  TractionSeparationLaw,
  VirtualCrackClosureTechnique,
  ExtendedFiniteElementMethod,
  XFEM,
  ContourIntegralMethod
 ]

 EXCLUDE_AS_PRIMARY = [
  PlasticYieldingWithoutCrackGrowth,
  FatigueLifeWithoutCrackMechanics,
  DamageMechanicsWithoutDiscreteCrackInterpretation,
  GeneralFailureTheoryWithoutFractureParameterContext
 ]

 DISAMBIGUATION_RULE =
  "When crack-tip fields, flaws, fracture toughness, energy release, crack growth or instability criteria are central to the analysis, interpret the context as fracture mechanics."
}

CORE_CONCEPTS {

 FractureMechanics {
  definition = "The mathematical framework for analysing cracks and fracture in solids and structures."
 }

 StressIntensityFactor {
  definition = "A parameter describing the amplitude of the near-tip singular stress field in linear elastic fracture mechanics."
 }

 FractureToughness {
  definition = "A material resistance measure against crack extension under a specified fracture mode and constraint state."
 }

 EnergyReleaseRate {
  definition = "The decrease in potential energy per unit increase in crack area."
 }

 JIntegral {
  definition = "A path-independent contour integral characterising crack-tip energy flow under suitable conditions."
 }

 ModeI {
  definition = "Opening-mode fracture with crack faces separating normally."
 }

 ModeII {
  definition = "Sliding-mode fracture with in-plane shear displacement."
 }

 ModeIII {
  definition = "Tearing-mode fracture with out-of-plane shear displacement."
 }

 CrackTipOpeningDisplacement {
  definition = "A crack-tip deformation measure used in elastic-plastic fracture assessment."
 }

 FatigueCrackGrowth {
  definition = "Progressive crack extension under repeated cyclic loading."
 }

 CohesiveZoneModel {
  definition = "A fracture model representing crack initiation and separation through a traction-separation relation."
 }
}

RELATIONS {
 FractureMechanics --is_child_of--> EngineeringMathematics
 Crack --has--> CrackTip
 Crack --has--> CrackFront
 ModeI --is_type_of--> FractureMode
 ModeII --is_type_of--> FractureMode
 ModeIII --is_type_of--> FractureMode
 StressIntensityFactor --characterises--> CrackTipField
 FractureToughness --limits--> StressIntensityFactor
 EnergyReleaseRate --measures--> CrackDrivingForce
 GriffithCriterion --uses--> EnergyReleaseRate
 JIntegral --characterises--> NonlinearCrackDrivingForce
 CrackTipOpeningDisplacement --characterises--> DuctileCrackTipDeformation
 SmallScaleYielding --supports--> LEFMApproximation
 PlasticZone --forms_near--> CrackTip
 FatigueCrackGrowth --depends_on--> DeltaK
 ParisLaw --models--> FatigueCrackGrowth
 CrackClosure --modifies--> EffectiveDeltaK
 ResidualStress --modifies--> CrackDrivingForce
 CohesiveZoneModel --regularises--> CrackTipSingularity
 XFEM --represents--> CrackWithoutConformingMesh
}

OPERATORS {
 MODE_I_STRESS_INTENSITY(Y,sigma,a) :=
  K_I=Y*sigma*sqrt(pi*a)

 MODE_II_STRESS_INTENSITY(Y,tau,a) :=
  K_II=Y*tau*sqrt(pi*a)

 CRITICAL_FRACTURE_CONDITION(K,K_c) :=
  K>=K_c

 ENERGY_RELEASE_RATE(Pi,A) :=
  G=-dPi/dA

 LEFM_RELATION_PLANE_STRESS(K,E) :=
  G=K^2/E

 LEFM_RELATION_PLANE_STRAIN(K,E,nu) :=
  G=K^2*(1-nu^2)/E

 GRIFFITH_CRITERION(G,G_c) :=
  crack_growth_if G>=G_c

 PARIS_LAW(C,m,DeltaK) :=
  da/dN=C*(DeltaK)^m

 STRESS_INTENSITY_RANGE(Kmax,Kmin) :=
  DeltaK=Kmax-Kmin

 R_RATIO(Kmin,Kmax) :=
  R=Kmin/Kmax

 IRWIN_PLASTIC_ZONE_PLANE_STRESS(K_I,sigma_y) :=
  r_p=(1/(2*pi))*(K_I/sigma_y)^2

 IRWIN_PLASTIC_ZONE_PLANE_STRAIN(K_I,sigma_y) :=
  r_p=(1/(6*pi))*(K_I/sigma_y)^2

 MIXED_MODE_EFFECTIVE_K(KI,KII,KIII) :=
  evaluate_using_declared_mixed_mode criterion
}

DEFINITIONS {
 D1 = "Fracture mechanics accounts explicitly for cracks or crack-like defects."
 D2 = "LEFM assumes predominantly linear elastic behaviour outside a small crack-tip process zone."
 D3 = "Stress intensity factors scale the singular near-tip field."
 D4 = "Fracture toughness defines a critical crack-driving threshold under specified conditions."
 D5 = "Energy release rate is an energetic measure of crack-driving force."
 D6 = "The J-integral extends crack-driving-force concepts into elastic-plastic regimes."
 D7 = "Plane strain generally produces higher crack-tip constraint than plane stress."
 D8 = "Fatigue crack growth depends strongly on cyclic stress-intensity range and load ratio."
 D9 = "Residual stresses can accelerate or retard crack growth."
 D10 = "Cohesive-zone and XFEM methods provide numerical alternatives to singular crack-tip modelling."
}

AXIOMS {
 A1_CRACK_DEPENDENCE:
  FractureMechanics requires an explicit crack flaw or crack-like discontinuity

 A2_TIP_FIELD:
  Crack-tip fields govern local fracture driving force

 A3_MODE_DEPENDENCE:
  Fracture response depends on mode I II III or mixed-mode loading

 A4_CRITICALITY:
  Crack growth occurs when an appropriate driving-force measure reaches a critical material resistance

 A5_CONSTRAINT:
  Fracture toughness depends on thickness geometry and crack-tip constraint

 A6_SMALL_SCALE_YIELDING:
  LEFM requires plastic deformation to remain sufficiently localised relative to crack and ligament dimensions

 A7_HISTORY:
  Fatigue crack growth depends on load history closure and environment

 A8_NUMERICAL_RESOLUTION:
  Numerical fracture analysis requires appropriate crack-tip enrichment mesh refinement or cohesive regularisation
}

REASONING {

 R1_FRACTURE_CONTEXT {
  INPUT = cracked_structure_or_material
  IDENTIFY = crack_geometry
  IDENTIFY = loading_mode
  IDENTIFY = material_properties
  IDENTIFY = thickness_and_constraint
  RETURN = fracture_context
 }

 R2_LEFM_VALIDITY {
  INPUT = fracture_context
  ESTIMATE = plastic_zone_size
  COMPARE = crack_length_ligament_and_thickness scales
  RETURN = LEFM_validity_status
 }

 R3_STRESS_INTENSITY_REASONING {
  INPUT = crack_geometry_load_and_boundary conditions
  COMPUTE = K_I_K_II_K_III
  RETURN = stress_intensity_profile
 }

 R4_ENERGY_REASONING {
  INPUT = cracked_system_energy
  COMPUTE = G_or_J
  COMPARE = critical_resistance
  RETURN = energy_fracture_status
 }

 R5_TOUGHNESS_REASONING {
  INPUT = K_or_J_or_CTOD_and_material toughness
  CHECK = validity_and_constraint requirements
  CLASSIFY = stable_or_critical
  RETURN = toughness_assessment
 }

 R6_MIXED_MODE_REASONING {
  INPUT = KI_KII_KIII
  SELECT = declared_mixed_mode criterion
  RETURN = mixed_mode_fracture_status
 }

 R7_FATIGUE_CRACK_GROWTH {
  INPUT = Kmax_Kmin_crack length_and_cycles
  COMPUTE = DeltaK_and_R
  APPLY = Paris_or_other growth law
  UPDATE = crack_length
  RETURN = fatigue_crack_growth profile
 }

 R8_ELASTIC_PLASTIC_REASONING {
  INPUT = significant_plasticity
  COMPUTE = JIntegral_CTOD_or_cohesive response
  RETURN = EPFM_profile
 }

 R9_NUMERICAL_FRACTURE {
  INPUT = mesh_crack_geometry_material_and_loading
  SELECT = contourIntegral_VCCT_XFEM_or_cohesive method
  COMPUTE = crack_driving parameters
  RETURN = numerical_fracture_result
 }

 R10_VALIDATION {
  INPUT = fracture_result
  CHECK = crack_geometry_mode_constraint_validity_mesh convergence_path independence_and_material data
  RETURN = validated_fracture_status
 }
}

CONSTRAINTS {
 C1 = "LEFM is invalid when plasticity is not sufficiently localised."
 C2 = "Fracture toughness values are not universal across thickness, orientation and environment."
 C3 = "Plane stress and plane strain fracture states must not be conflated."
 C4 = "Stress singularities require fracture-specific interpretation rather than ordinary peak-stress comparison."
 C5 = "Mixed-mode fracture requires an explicit interaction criterion."
 C6 = "Paris law is valid only within an intermediate fatigue crack-growth regime."
 C7 = "Threshold and near-instability fatigue regions may require different growth laws."
 C8 = "Residual stress can alter effective crack-driving force."
 C9 = "J-integral path independence depends on constitutive and loading assumptions."
 C10 = "Cohesive-zone results depend on traction-separation parameters and mesh regularisation."
}

SEMANTIC_EQUIVALENCE {
 "FractureMechanics" <=> "CrackMechanics"
 "StressIntensityFactor" <=> "SIF"
 "FractureToughness" <=> "CriticalCrackResistance"
 "EnergyReleaseRate" <=> "CrackEnergyReleaseRate"
 "CrackTipOpeningDisplacement" <=> "CTOD"
 "ExtendedFiniteElementMethod" <=> "XFEM"
}

VALIDATION {
 V1 = "Crack geometry and orientation are explicit."
 V2 = "Loading mode is identified."
 V3 = "LEFM or EPFM validity is justified."
 V4 = "Material toughness property matches constraint and environment."
 V5 = "Stress-intensity or energy calculations are geometry-consistent."
 V6 = "Mixed-mode criteria are documented where required."
 V7 = "Fatigue crack-growth law is used within its calibration range."
 V8 = "Residual-stress effects are included when relevant."
 V9 = "Numerical crack-tip or cohesive results are mesh-converged."
 V10 = "J-integral or contour results are checked for path independence where applicable."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 FRACTURE_MECHANICS_DEFINITION = 0.99
 LEFM_VALIDITY_REASONING = 0.98
 STRESS_INTENSITY_REASONING = 0.99
 ENERGY_REASONING = 0.99
 TOUGHNESS_REASONING = 0.98
 MIXED_MODE_REASONING = 0.97
 FATIGUE_GROWTH_REASONING = 0.98
 ELASTIC_PLASTIC_REASONING = 0.98
 NUMERICAL_FRACTURE_REASONING = 0.98

 POLICY =
  "Reduce confidence when crack geometry, loading mode, thickness, constraint, material toughness, residual stress, growth-law calibration, process-zone size or numerical crack-tip resolution are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  FractureMechanicsReasoning,
  LEFMReasoning,
  EPFMReasoning,
  StressIntensityReasoning,
  FractureToughnessReasoning,
  EnergyReleaseRateReasoning,
  JIntegralReasoning,
  CTODReasoning,
  MixedModeReasoning,
  PlasticZoneReasoning,
  FatigueCrackGrowthReasoning,
  ParisLawReasoning,
  CrackClosureReasoning,
  CohesiveZoneReasoning,
  XFEMReasoning,
  StructuralIntegrityReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]

 NORMALISE {
  "fracture mechanics" -> FractureMechanics
  "linear elastic fracture mechanics" -> LinearElasticFractureMechanics
  "LEFM" -> LinearElasticFractureMechanics
  "elastic-plastic fracture mechanics" -> ElasticPlasticFractureMechanics
  "EPFM" -> ElasticPlasticFractureMechanics
  "stress intensity factor" -> StressIntensityFactor
  "fracture toughness" -> FractureToughness
  "energy release rate" -> EnergyReleaseRate
  "J-integral" -> JIntegral
  "CTOD" -> CrackTipOpeningDisplacement
 }

 INTERPRETATION_ORDER = [
  detect_fracture_mechanics_context,
  identify crack_geometry_loading_mode_material_thickness_constraint_and_environment,
  assess LEFM_or_EPFM applicability,
  compute stress_intensity_energy_release_J_or_CTOD measure,
  compare crack_driving_force_with_fracture resistance,
  if_mixedMode apply interaction criterion,
  if_cyclic evaluate DeltaK_R_and_crack growth law,
  if_numerical use contour_integral_VCCT_XFEM_or_cohesive method,
  validate constraint_mesh_path_independence_and_material data,
  return semantic output
 ]
}

EXECUTION_RULES {
 E1:
  IF query_mentions("fracture mechanics")
  OR crack_tip_failure_analysis_is_present
  THEN activate(FractureMechanicsOntology)

 E2:
  IF plastic_zone_is_small_relative_to_crack_and_ligament
  THEN permit LEFM reasoning

 E3:
  IF significant_crack_tip_plasticity
  THEN use EPFM_JIntegral_or_CTOD pathway

 E4:
  IF K>=Kc
  THEN classify fracture_instability_subject_to_validity conditions

 E5:
  IF G>=Gc
  THEN classify crack_growth energetically_admissible

 E6:
  IF cyclic_loading
  THEN compute DeltaK_and_use fatigue_crack_growth model

 E7:
  IF mixed_mode_loading
  THEN require mixed_mode interaction criterion

 E8:
  IF residual_stress_present
  THEN include in crack_driving_force

 E9:
  IF numerical_crack_analysis
  THEN verify mesh_enrichment_or_cohesive regularisation
}

RECURSION {
 ENTRY = FractureMechanics

 EXPAND(FractureMechanics) -> [
  Crack,
  CrackTip,
  CrackFront,
  CrackLength,
  CrackGrowth,
  CrackInitiation,
  StableCrackGrowth,
  UnstableFracture,
  BrittleFracture,
  DuctileFracture,
  LinearElasticFractureMechanics,
  ElasticPlasticFractureMechanics,
  ModeI,
  ModeII,
  ModeIII,
  MixedModeFracture,
  StressIntensityFactor,
  K_I,
  K_II,
  K_III,
  FractureToughness,
  K_IC,
  EnergyReleaseRate,
  CriticalEnergyReleaseRate,
  GriffithCriterion,
  JIntegral,
  J_IC,
  CrackTipOpeningDisplacement,
  ProcessZone,
  PlasticZone,
  SmallScaleYielding,
  PlaneStressFracture,
  PlaneStrainFracture,
  CrackTipSingularity,
  WilliamsExpansion,
  TStress,
  FatigueCrackGrowth,
  DeltaK,
  ParisLaw,
  ThresholdStressIntensityRange,
  CrackClosure,
  RRatio,
  ResidualStress,
  EnvironmentalFracture,
  StressCorrosionCracking,
  CohesiveZoneModel,
  TractionSeparationLaw,
  VirtualCrackClosureTechnique,
  ExtendedFiniteElementMethod,
  ContourIntegralMethod
 ]

 EXPAND(FractureParameters) -> [
  StressIntensityFactor,
  FractureToughness,
  EnergyReleaseRate,
  JIntegral,
  CrackTipOpeningDisplacement,
  TStress
 ]

 EXPAND(NumericalMethods) -> [
  ContourIntegralMethod,
  VirtualCrackClosureTechnique,
  ExtendedFiniteElementMethod,
  CohesiveZoneModel
 ]

 STOP_CONDITION =
  "Stop when crack geometry, fracture mode, governing crack-driving parameter, material resistance, validity regime, growth law, constraint and numerical validation are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Engineering Mathematics"

 IMMEDIATE_CONTEXTS = [
  "Engineering Mathematics Ontology",
  "Stress Analysis Ontology",
  "Strain Analysis Ontology",
  "Elasticity Ontology",
  "Plasticity Ontology"
 ]

 RELATED_ONTOLOGIES = [
  "Engineering Mathematics",
  "Engineering Mathematics Ontology",
  "Structural Analysis Ontology",
  "Stress Analysis Ontology",
  "Strain Analysis Ontology",
  "Elasticity Ontology",
  "Plasticity Ontology",
  "Solid Mechanics Ontologies",
  "Continuum Mechanics Ontologies",
  "Fatigue Ontologies",
  "Failure Theory Ontologies",
  "Finite Element Ontology",
  "Materials Science Ontologies",
  "Numerical Analysis Ontologies"
 ]

 ROUTE_RULES = [
  "Fracture Mechanics -> Engineering Mathematics for parent semantics",
  "Fracture Mechanics -> Stress Analysis for crack-tip stress fields",
  "Fracture Mechanics -> Strain Analysis for crack-tip deformation",
  "Fracture Mechanics -> Elasticity for LEFM fields",
  "Fracture Mechanics -> Plasticity for EPFM and crack-tip yielding",
  "Fracture Mechanics -> Structural Analysis for structural integrity",
  "Fracture Mechanics -> Fatigue for cyclic crack growth",
  "Fracture Mechanics -> Failure Theory for instability criteria",
  "Fracture Mechanics -> Finite Element for contour integrals, VCCT, XFEM and cohesive models",
  "Fracture Mechanics -> Materials Science for toughness and environmental effects"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"

 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible fracture parameters, growth models or numerical pathways"
 PATCH = "clarification, metadata or formatting correction"

 RULES = [
  "Preserve explicit-crack semantics.",
  "Preserve LEFM-versus-EPFM distinction.",
  "Preserve mode-I-II-III distinction.",
  "Preserve crack-driving-force versus material-resistance semantics.",
  "Preserve plane-stress-versus-plane-strain constraint distinction.",
  "Preserve fatigue-crack-growth semantics.",
  "Preserve numerical crack-representation semantics.",
  "Preserve machine-readable fracture-mechanics semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION =
  "Fracture mechanics analyses crack initiation, crack growth and instability using crack-tip stress, energy and deformation measures."

 LEFM_SUMMARY =
  "LEFM characterises near-tip fields using stress intensity factors when plastic deformation is sufficiently localised."

 ENERGY_SUMMARY =
  "Energy release rate measures the energetic driving force for crack extension."

 EPFM_SUMMARY =
  "Elastic-plastic fracture mechanics uses J-integral and CTOD measures when crack-tip plasticity is significant."

 TOUGHNESS_SUMMARY =
  "Fracture toughness is the material resistance compared against the selected crack-driving parameter."

 FATIGUE_SUMMARY =
  "Fatigue crack growth is commonly correlated with cyclic stress-intensity range and load ratio."

 NUMERICAL_SUMMARY =
  "Contour integrals, VCCT, XFEM and cohesive-zone methods provide numerical fracture-analysis pathways."

 VALIDATION_SUMMARY =
  "Fracture assessments should be checked for crack geometry, mode mixity, constraint, material data, validity regime and numerical convergence."
}

FLOW {
 INPUT
 -> detect_fracture_mechanics_context
 -> identify crack_geometry_orientation_length_loading_mode_material toughness_thickness_constraint_environment_and_load history
 -> determine LEFM_EPFX_or_cohesive applicability
 -> compute KI_KII_KIII_G_J_CTOD_or_other crack-driving measure
 -> compare driving_force_with_critical material resistance
 -> if_mixedMode apply interaction criterion
 -> if_fatigue compute DeltaK_R_ratio_and_incremental crack growth
 -> if_residual_or_environmental effects include modified crack-driving or resistance
 -> if_numerical choose contourIntegral_VCCT_XFEM_or_cohesiveZone method
 -> validate validity regime_constraint_path independence_mesh convergence_and_material calibration
 -> route to engineering_mathematics structural_analysis stress_analysis strain_analysis elasticity plasticity solid_mechanics continuum_mechanics fatigue failure_theory finite_element materials_science_or_numerical_analysis ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Fracture Mechanics Ontology defines mathematical crack analysis in solids and structures. It supports cracks, crack tips and fronts, crack initiation and propagation, brittle and ductile fracture, linear elastic and elastic-plastic fracture mechanics, modes I, II and III, mixed-mode fracture, stress intensity factors and fracture toughness, energy release rate and Griffith theory, J-integral and CTOD, plastic and process zones, plane-stress and plane-strain constraint, crack-tip singular fields and T-stress, fatigue crack growth, DeltaK, Paris law, threshold behaviour, crack closure and load ratio, residual and environmental effects, cohesive-zone models, VCCT, XFEM and contour-integral methods."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-FRACTURE-MECHANICS-ONTOLOGY-V1"
}

}

END_FLOW