Poisson's ratio
Enable an agent to identify, interpret, compare and appropriately use Poisson's ratio as a measure of transverse deformation relative to axial deformation.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
recalled by Codex without web access - no source was read
Researched by: Codex
Purpose and description
Enable an agent to identify, interpret, compare and appropriately use Poisson's ratio as a measure of transverse deformation relative to axial deformation.
Poisson's ratio is the dimensionless negative ratio of transverse normal strain to axial normal strain under uniaxial stress, conventionally specified in the small-strain elastic regime and for stated loading and transverse directions.
It can be Determine whether a reported number is a Poisson's ratio and identify its precise interpretation.; Calculate a strain ratio from compatible axial and transverse measurements with an explicit sign convention.; Compare reported values after aligning directions, strain definitions and test conditions.; Check a value against the admissibility conditions of its stated constitutive model.; Select a supported value for a calculation or identify missing evidence that prevents its use.; Flag apparent auxetic behaviour for examination of measurement quality, material scale and loading constraints..
Distinguishing features
The numerator is transverse normal strain and the denominator is axial normal strain, with a leading minus sign under the usual convention.
A material-property interpretation requires specified loading conditions; an arbitrary ratio of strains in a constrained specimen is insufficient.
It is dimensionless and describes coupling between perpendicular normal strains, rather than stiffness or volumetric strain alone.
For anisotropic materials, the loading direction and transverse observation direction identify the ratio; a single scalar may be insufficient.
A negative value denotes transverse expansion during axial tension under the stated conditions and is not automatically a measurement error.
Scope
+ Definition as the negative ratio of transverse strain to axial strain under specified uniaxial loading conditions.
+ Distinction between an elastic material constant and a condition-dependent or apparent strain ratio.
+ Directional dependence and the distinction between isotropic and anisotropic descriptions.
+ Measurement, estimation, uncertainty and traceability of reported values.
+ Compatibility with constitutive assumptions and intended engineering calculations.
- The general mathematical concept of ratio.
- Complete material characterisation or a full constitutive model.
- Independent models of Young's modulus, shear modulus and bulk modulus.
- Structural deformation governed primarily by geometry, supports or contact.
- Poisson distributions, Poisson processes and Poisson's equation.
Characteristics
- Reported ratio
- Dimensionless; retain uncertainty and reporting precision. Provides the numerical quantity while preventing unsupported precision.
- Ratio interpretation
- Small-strain elastic constant; secant strain ratio; incremental strain ratio; dynamic response quantity; apparent ratio. Separates quantities that can share a name but cannot necessarily be substituted for one another.
- Loading and transverse directions
- Ordered pair of perpendicular directions tied to specimen and material coordinates. Identifies which directional coupling was measured or modelled.
- Strain definition and evaluation interval
- Named strain measure, reference configuration and strain interval or evaluation point. Makes values interpretable when deformation is nonlinear or no longer infinitesimal.
- Constitutive symmetry
- Isotropic; transversely isotropic; orthotropic; general anisotropic; unresolved. Determines whether one ratio is sufficient and which consistency relations apply.
- Loading and environmental conditions
- Stress state, temperature, strain rate or frequency, elapsed time and relevant material conditioning, each with units. Defines the conditions under which the reported response applies.
- Represented material scale
- Constituent; local region; homogenised material; effective cellular medium; specimen-level apparent response. Prevents a geometry-dependent response from being mistaken for an intrinsic constituent property.
- Evidence basis
- Direct strain measurement; elastic-constant derivation; inverse identification; simulation; cited reference value. Exposes the observations and assumptions behind the value.
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 6 bundles · 11 layers · 17 findings · 27 questions.
Strain ratio meaning Establishes what the named ratio measures and which interpretation is intended.
The general concept of ratio does not supply the strain operands, mechanical conditions or sign convention that distinguish Poisson's ratio.
Operands and sign
Identifies the axial and transverse strains and their sign conventions.
Negative transverse-to-axial ratio
Record the definition used, ordinarily ν = −ε_transverse/ε_axial, and the loading conditions that make it meaningful.
- Which measured or modelled normal strains are the numerator and denominator, and how are their signs defined? definition
- Does the loading condition support interpreting this ratio as Poisson's ratio rather than an arbitrary strain response? boundary
Constant or response
Separates a small-strain elastic parameter from ratios evaluated along more general deformation histories.
Declared ratio interpretation
Record whether the value is an elastic constant, a secant ratio, an incremental ratio or another explicitly defined response quantity.
- Is the value obtained from total strains, strain increments or a fitted slope over an elastic interval? definition
- Which strain measure, reference configuration and evaluation interval make this interpretation reproducible? measurement
Direction and material scale Identifies the material directions and scale to which the ratio belongs.
Direction and homogenisation can change the meaning of a value even when its numerical magnitude is unchanged.
Directional coupling
Connects the axial loading direction to the transverse observation direction.
Ordered direction pair
Record both directions and the source's index convention instead of assuming that subscripts are used consistently across references.
- Which direction is loaded and which perpendicular direction supplies the transverse strain? definition
- What evidence supports treating the material as isotropic or equating ratios measured in different directions? boundary
Constituent and effective response
Distinguishes local material coupling from an effective response of a heterogeneous or cellular medium.
Represented scale and volume
Identify whether the ratio describes a constituent, a sampled region, a homogenised medium or the deformation of a particular specimen.
- What material volume or structural region does the reported ratio represent? provenance
- Could specimen geometry, cell arrangement or boundary effects explain the value without establishing a transferable material property? boundary
Determination and uncertainty Captures how the ratio was obtained and whether the evidence resolves the transverse response.
Small transverse strains, loading imperfections and inferred values require different checks before a number can be trusted.
Strain observation
Examines paired strain measurements and the loading arrangement.
Paired strain evidence
Record instrumentation, measurement regions, synchronisation and checks for departures from the intended stress state.
- How were axial and transverse strains measured over compatible regions and loading intervals? measurement
- How were bending, misalignment, grip constraints and insufficient transverse strain resolution assessed? measurement
Estimation and traceability
Connects a reported value to its calculation, uncertainty and source evidence.
Derivation and confidence
Distinguish direct measurement from derivation or inverse fitting, retaining the assumptions and uncertainty of each route.
- Which data, source passage or fitted model produced the reported value, and which assumptions entered the calculation? provenance
- How do strain uncertainty, correlation between measurements and the choice of fitting interval affect uncertainty in the ratio? measurement
Constitutive consistency Checks whether the value is admissible and mutually consistent with the assumed elastic description.
Bounds and modulus relationships are conditional on the constitutive model and must not be applied universally.
Isotropic elastic relations
Applies familiar bounds and modulus conversions only within their stated assumptions.
Isotropic assumption check
For stable three-dimensional isotropic linear elasticity with positive finite bulk and shear moduli, check −1 < ν < 0.5 and consistency with E = 2G(1 + ν) and E = 3K(1 − 2ν).
- Are isotropy, linear elasticity and the three-dimensional constitutive interpretation justified for this value? boundary
- Are available Young's, shear and bulk moduli consistent with the reported ratio under matching conditions? measurement
Anisotropic and limiting cases
Handles directional coupling, auxetic response and incompressible limits without imposing inappropriate scalar rules.
Model-specific admissibility
Assess directional ratios within the full constitutive description; distinguish negative response from instability and an incompressible idealisation from a finite compressibility measurement.
- For an anisotropic elastic model, do the directional ratios and moduli satisfy the applicable reciprocity and stability conditions? boundary
- Does an unusual or limiting value represent supported material behaviour, an idealisation or an inconsistent parameter set? action
Conditions and use Defines when a value remains applicable and how an agent may use it.
A valid measurement can still be unsuitable for a calculation performed at another rate, temperature, deformation regime or constraint state.
Response dependence
Records conditions that may alter the transverse-to-axial response.
Conditioned applicability
Associate the ratio with temperature, material conditioning, loading history and time or frequency where relevant.
- Over which temperatures, strain amplitudes, rates and loading histories is this value supported? boundary
- For time-dependent or oscillatory response, how are elapsed time, frequency and any phase difference incorporated into the definition? definition
Calculation readiness
Matches an available ratio to the assumptions and sensitivity of an intended calculation.
Supported parameter selection
Determine whether a candidate ratio can be used directly, requires conversion under justified assumptions or needs further evidence.
- Does the intended calculation require the same direction pair, material scale, response regime and strain interpretation as the available value? action
- How sensitive is the result to uncertainty in this ratio, particularly when the model approaches incompressibility? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- This is recalled knowledge; no sources or current standard editions were consulted.
- Material-specific values require verification of direction, temperature, strain regime and measurement conditions.
- For anisotropic, nonlinear or time-dependent materials, verify the precise definition and convention used; a single constant may be insufficient.
- Which of these check these first hold for the sense of Poisson's ratio this model covers, and on what evidence? provenance
Kinds and varieties
Recalled without web access and unsourced; every item is a lead to verify.
- Isotropic Poisson's ratio
- Directional Poisson's ratios in anisotropic materials
- Effective Poisson's ratio of composites or structured materials
- Negative Poisson's ratio associated with auxetic behaviour
- Which of these kinds and varieties hold for the sense of Poisson's ratio this model covers, and on what evidence? provenance
Standards and regulation
Recalled without web access and unsourced; every item is a lead to verify.
- ASTM International ASTM E132: Standard Test Method for Poisson's Ratio at Room Temperature.
- Which of these standards and regulation hold for the sense of Poisson's ratio this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Predicting lateral contraction or expansion under axial loading.
- Specifying elastic constitutive models for structural and finite-element analysis.
- Relating elastic moduli in isotropic linear elasticity.
- Characterising composites, foams and auxetic structures.
- Interpreting elastic-wave measurements alongside density and other elastic properties.
- Which of these real-world use hold for the sense of Poisson's ratio this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Poisson's ratio, ν = −ε_transverse/ε_axial - Many metals are approximately 0.25-0.35; nearly incompressible elastic materials approach 0.5. - dimensionless
- Poisson's ratio for a stable isotropic linear-elastic solid with finite positive bulk and shear moduli - Theoretical admissible interval: −1 < ν < 0.5; this is not a universal bound for directional values in anisotropic solids. - dimensionless
- Which of these typical measurements hold for the sense of Poisson's ratio this model covers, and on what evidence? provenance
Failure modes and hazards
Recalled without web access and unsourced; every item is a lead to verify.
- Omitting the minus sign reverses the interpretation of ordinary and auxetic behaviour.
- Using a single isotropic value for an anisotropic material can misrepresent its deformation.
- Applying a small-strain elastic value during plastic deformation or large strains can produce inaccurate predictions.
- Treating values as independent of temperature, loading rate or frequency can be misleading, particularly for polymers and viscoelastic materials.
- Using unsuitable finite-element formulations near incompressibility can cause volumetric locking and artificially stiff predictions.
- Which of these failure modes and hazards hold for the sense of Poisson's ratio this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- ratio - A ratio is a general quotient; Poisson's ratio specifies a signed quotient of transverse and axial strains under defined loading conditions.
- Young's modulus - Young's modulus relates axial stress to axial strain and has pressure units; Poisson's ratio relates transverse to axial strain and is dimensionless.
- bulk modulus - Bulk modulus measures resistance to volumetric deformation under hydrostatic loading; Poisson's ratio describes transverse response under uniaxial stress.
- shear modulus - Shear modulus relates shear stress to shear strain; Poisson's ratio couples normal strains in different directions.
- auxetic behaviour - Auxetic behaviour denotes expansion transversely when stretched, corresponding to a negative Poisson's ratio for the specified directions and conditions.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of Poisson's ratio this model covers, and on what evidence? provenance
What the second pass must settle
- Which authoritative references and measurement standards should anchor the registry definition and distinguish elastic, incremental, finite-strain and dynamic uses of the name?
- Does an existing Vercy world model already cover Poisson's ratio, requiring this registry entry to link to that publication?
- Should effective ratios of cellular materials remain within this model under an explicit scale qualifier, or link to a separate effective-property model?
- Which directional index convention should the publication adopt, and how should differing source conventions be translated?
- How should time-dependent and complex dynamic ratios be represented without implying equivalence to a single elastic constant?