Stress Ontology

# Stress Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/stress-ontology.html

FLOW StressOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Mechanical Measurements
    -> Stress Ontology

  PURPOSE:
    Represent mechanical stress as an internal force-intensity quantity within a material or continuum, including normal and shear stress, tensile and compressive states, stress tensors, principal stresses, units, dimensional structure, traction, strain relationships, constitutive behaviour, measurement conditions, uncertainty, and distinctions from pressure and externally applied force.

  ENTITY Stress {
    TYPE: DerivedContinuumMechanicalQuantity
    SYMBOL: sigma
    DIMENSION: M * L^-1 * T^-2
    SI_UNIT: pascal
    SI_SYMBOL: Pa

    SIMPLE_AVERAGE_FORM:
      sigma = F / A

    CONTINUUM_DEFINITION:
      stress := local_internal_force_per_unit_area_with_directional_dependence

    GENERAL_REPRESENTATION:
      CauchyStressTensor

    PROPERTIES:
      is_second_order_tensor_in_general_three_dimensional_continuum
      has_normal_components
      has_shear_components
      has_unit
      has_dimension
      depends_on_orientation
      may_vary_with_position
      may_vary_with_time
      may_have_uncertainty
  }

  ENTITY NormalStress {
    TYPE: StressComponent
    SYMBOL: sigma_n

    DEFINITION:
      component_of_traction_normal_to_surface

    CLASSIFICATION:
      tensile_stress
      compressive_stress
  }

  ENTITY ShearStress {
    TYPE: StressComponent
    SYMBOL: tau

    DEFINITION:
      component_of_traction_tangential_to_surface
  }

  ENTITY Force {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: F
    DIMENSION: M * L * T^-2

    RELATION:
      Force / Area -> AverageStress
  }

  ENTITY Area {
    TYPE: DerivedGeometricQuantity
    SYMBOL: A
    DIMENSION: L^2

    RELATION:
      Force / Area -> AverageStress
  }

  ENTITY Strain {
    TYPE: DimensionlessMechanicalQuantity
    SYMBOL: epsilon

    RELATION:
      Stress -> RELATED_BY_CONSTITUTIVE_MODEL_TO -> Strain
  }

  ENTITY Pressure {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: p
    DIMENSION: M * L^-1 * T^-2

    RELATION:
      isotropic_fluid_stress_state -> related_to Pressure
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: pascal
      symbol: Pa

      equivalence:
        1 Pa = 1 N/m^2
        1 Pa = 1 kg/(m*s^2)
    }

    ENGINEERING_UNITS {
      kilopascal
      megapascal
      gigapascal
      newton_per_square_millimetre
      pounds_per_square_inch
      ksi
    }

    COMMON_EQUIVALENCE:
      1 MPa = 1 N/mm^2

    CONVERSION_RULE:
      stress_value(target_unit)
        = stress_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by_component:
      normal_stress
      shear_stress

    by_normal_loading:
      tensile_stress
      compressive_stress

    by_distribution:
      uniform_stress
      nonuniform_stress
      local_stress
      average_stress

    by_analysis:
      principal_stress
      hydrostatic_stress
      deviatoric_stress
      equivalent_stress
  }

  STRESS_TENSOR_MODEL {
    CAUCHY_STRESS_TENSOR:
      sigma_tensor =
        [[sigma_xx, tau_xy, tau_xz],
         [tau_yx, sigma_yy, tau_yz],
         [tau_zx, tau_zy, sigma_zz]]

    TRACTION_RELATION:
      traction(n) = sigma_tensor * n

    CLASSICAL_ANGULAR_MOMENTUM_BALANCE:
      sigma_tensor = transpose(sigma_tensor)
      WHEN classical_continuum_without_couple_stresses

    COMPONENT_MEANING:
      diagonal_terms -> normal_stresses
      off_diagonal_terms -> shear_stresses
  }

  PRINCIPAL_STRESS_MODEL {
    DEFINITION:
      principal_stresses := eigenvalues(CauchyStressTensor)

    PRINCIPAL_DIRECTIONS:
      eigenvectors(CauchyStressTensor)

    PROPERTY:
      shear_components_on_principal_planes = 0

    VALUES:
      sigma_1
      sigma_2
      sigma_3
  }

  HYDROSTATIC_DEVIATORIC_MODEL {
    MEAN_STRESS:
      sigma_mean = trace(sigma_tensor) / 3

    HYDROSTATIC_COMPONENT:
      sigma_h = sigma_mean * IdentityTensor

    DEVIATORIC_COMPONENT:
      s = sigma_tensor - sigma_h

    RULE:
      sign_convention MUST be identified
      when relating mean_stress_to_pressure
  }

  PRESSURE_DISTINCTION_MODEL {
    pressure:
      scalar_quantity_for_isotropic_normal_compression_in_fluid_context

    stress:
      general_tensor_quantity_with_normal_and_shear_components

    STATIC_FLUID_RELATION:
      sigma_tensor = -p * IdentityTensor
      UNDER common_tension_positive_sign_convention

    RULE:
      pressure MUST_NOT be treated_as_general_solid_stress
  }

  STRESS_STRAIN_MODEL {
    GENERAL:
      stress = constitutive_function(strain, strain_rate, temperature, history, material_state)

    LINEAR_ELASTIC_UNIAXIAL:
      sigma = E * epsilon

    PARAMETER:
      E = YoungsModulus

    CONDITIONS:
      linear_elastic_regime
      uniaxial_idealisation
      applicable_material_model
  }

  RELATIONSHIPS {
    Stress -> INTERNAL_FORCE_INTENSITY_OVER -> Area
    Stress -> HAS_DIMENSION -> M*L^-1*T^-2
    Stress -> MEASURED_IN -> Pascal
    StressTensor -> MAPS -> SurfaceNormalToTraction
    NormalStress -> COMPONENT_OF -> StressTensor
    ShearStress -> COMPONENT_OF -> StressTensor
    Stress -> RELATED_TO -> Strain
    Stress -> DEPENDS_ON -> MaterialConstitutiveBehaviour
    PrincipalStress -> EIGENVALUE_OF -> StressTensor
    Pressure -> SPECIAL_ISOTROPIC_RELATION_TO -> StressTensor
  }

  SEMANTIC_EQUIVALENCE {
    "pascal" ~= "Pa"
    "newton per square metre" ~= "N/m^2"
    "megapascal" ~= "N/mm^2"
    "normal stress" != "shear stress"
    stress != force
    stress != strain
    stress != pressure
    stress != elastic_modulus
  }

  CONSTRAINTS {
    dimensional_formula = M*L^-1*T^-2
    SI_unit = Pa
    general_stress_is_tensor_quantity = true
    simple_force_area_ratio_is_context_dependent_average_idealisation = true
    surface_orientation_matters_for_traction_and_stress_components = true
    stress_and_pressure_are_not_generally_semantically_equivalent = true
    stress_and_strain_are_not_semantically_equivalent = true
    sign_convention_must_be_preserved = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      Stress

    COMMON_INFERENCE_METHODS:
      applied_force_divided_by_cross_sectional_area
      strain_gauge_plus_constitutive_relation
      load_cell_plus_geometry
      photoelastic_measurement
      digital_image_correlation_plus_material_model
      finite_element_inverse_or_computational_analysis

    RECORD:
      numerical_value_or_tensor
      unit
      stress_type
      tensor_components
      principal_values
      material
      geometry
      area
      force_or_load
      surface_orientation
      spatial_location
      timestamp
      temperature_when_relevant
      constitutive_model
      sign_convention
      measurement_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_stress = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF axial_force_known AND cross_section_area_known AND area != 0
      AND uniform_uniaxial_assumption_valid
      THEN average_normal_stress = axial_force / cross_section_area

    IF shear_force_known AND shear_area_known AND area != 0
      AND uniform_shear_assumption_valid
      THEN average_shear_stress = shear_force / shear_area

    IF stress_tensor_known AND surface_normal_known
      THEN traction_vector = stress_tensor * surface_normal

    IF stress_tensor_known
      THEN principal_stresses = eigenvalues(stress_tensor)

    IF linear_elastic_uniaxial_conditions_apply
      AND Youngs_modulus_known
      AND strain_known
      THEN stress = Youngs_modulus * strain

    IF static_fluid_pressure_known
      THEN stress_tensor = -pressure * identity_tensor
      UNDER tension_positive_sign_convention

    IF stress_tensor_known
      THEN mean_stress = trace(stress_tensor)/3
      AND deviatoric_stress = stress_tensor - mean_stress*identity_tensor
  }

  MATERIAL_CONTEXT_MODEL {
    REQUIRE_WHEN_RELEVANT:
      material_identity
      constitutive_model
      temperature
      strain_rate
      loading_history
      phase_or_microstructure

    RULE:
      same_strain MAY correspond_to_different_stress
      for_different_material_models_or_histories
  }

  GEOMETRY_MODEL {
    REQUIRE:
      cross_section_or_surface_geometry
      load_direction
      coordinate_system
      point_or_region_of_interest

    STRESS_CONCENTRATION:
      local_stress MAY greatly_exceed nominal_average_stress
      near_geometric_discontinuities

    RULE:
      nominal_stress MUST_NOT automatically_replace local_stress
  }

  FAILURE_CONTEXT_MODEL {
    possible_derived_measures:
      maximum_principal_stress
      maximum_shear_stress
      von_Mises_equivalent_stress

    RULE:
      failure_prediction_requires_material_specific_failure_criterion
      AND applicable_loading_context

    CONSTRAINT:
      equivalent_stress_is_derived_scalar
      NOT replacement_for_full_stress_tensor
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    tensor_relationship_confidence: 1.00
    constitutive_relationship_confidence: 0.98
    measurement_context_confidence: 0.97

    RULE:
      confidence decreases when stress type, geometry, material,
      surface orientation, coordinate system, constitutive model,
      sign convention, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK area_nonzero_for_force_area_calculation
    CHECK stress_type
    CHECK tensor_component_coordinate_system
    CHECK surface_orientation_for_traction
    CHECK sign_convention
    CHECK material_constitutive_model_when_stress_inferred_from_strain
    CHECK nominal_vs_local_stress_semantics
    CHECK stress_pressure_distinction
    CHECK stress_strain_distinction
    CHECK instrument_calibration_when_measured
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_stress_type
      identify_material_and_geometry
      identify_coordinate_system
      identify_sign_convention
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_spatial_location
      attach_timestamp
      attach_uncertainty
      update_stress_state

    ON load_or_geometry_change:
      update_force_or_boundary_conditions
      update_geometry
      recompute_nominal_or_local_stress
      update_tensor_state
      recompute_principal_stresses_when_required

    ON constitutive_model_change:
      preserve_previous_model
      update_material_parameters
      recompute_inferred_stresses
      update_confidence

    ON revised_calibration:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Stress
    canonical_symbol: sigma
    canonical_dimension: M*L^-1*T^-2
    canonical_SI_unit: Pa

    interpretation_order:
      identify_quantity
      identify_stress_type
      identify_value_or_tensor
      identify_unit
      identify_material
      identify_geometry
      identify_coordinate_system
      identify_surface_orientation
      identify_load_or_force
      identify_sign_convention
      identify_constitutive_context
      identify_measurement_or_inference_method
      identify_uncertainty
      validate_dimensions
      infer_tensor_and_material_relationships

    ambiguity_controls:
      distinguish_stress_from_force
      distinguish_stress_from_pressure
      distinguish_stress_from_strain
      distinguish_normal_from_shear_stress
      distinguish_tensile_from_compressive_stress
      distinguish_nominal_from_local_stress
      distinguish_tensor_stress_from_equivalent_scalar_stress
      distinguish_material_response_from_applied_load
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_mechanical_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Mechanical Measurements
      -> Stress Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      stress_tensor_model
      principal_stress_model
      hydrostatic_deviatoric_model
      pressure_distinction_model
      stress_strain_model
      material_context_model
      geometry_model
      failure_context_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      tensor_model_changes
      constitutive_model_changes
      material_context_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW