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InformationUDP datagram service

UDP exchanges addressed messages without adding reliable stream delivery.

DefinitionInformationDNS names, records and caching

DNS distributes typed resource records through a delegated naming hierarchy.

DefinitionInformationCombinational digital-circuit model

A combinational output depends on current valid inputs after a bounded settling delay.

ModelInformationBoolean gates and truth tables

Logic gates compute Boolean functions with truth values 0 and 1.

DefinitionInformationClocked storage and sequential state

Sequential circuits retain state, so current inputs alone do not determine their behavior.

ModelInformationStored programs and instruction sets

Stored instructions control computation through a specified hardware/software interface.

ModelPhysicsDisplacement, distance and average speed

Displacement compares endpoints; distance measures the travelled path.

ModelPhysicsConstant-acceleration kinematics

Closed formulas require constant acceleration over the interval.

ModelPhysicsInertial reference frames and inertia

Newtonian force balances need an inertial frame or explicit inertial terms.

ModelPhysicsCircular motion and centripetal acceleration

A constant speed can still have an acceleration.

ModelPhysicsMass, gravitational weight and apparent weight

Mass is in kilograms; gravitational weight is a force.

ModelPhysicsNormal forces and tension

Contact geometry determines the force direction.

ModelPhysicsFree-body diagrams and system boundaries

List forces on the selected body once.

ModelPhysicsStatic and kinetic dry friction

Static friction is a responsive force with an approximate limit.

ModelPhysicsFluid drag and terminal speed

Terminal speed depends on the chosen drag model.

ModelPhysicsImpulse and momentum transfer

Time-integrated net force changes momentum.

ModelPhysicsElastic and inelastic collisions

Momentum conservation and kinetic-energy conservation are different.

ModelPhysicsConservative forces and potential energy

Potential-energy differences encode path-independent work.

ModelPhysicsMechanical-energy conservation and dissipation

Mechanical energy is only part of the total energy.

ModelPhysicsHooke’s spring model and elastic energy

A linear spring restores displacement toward equilibrium.

ModelPhysicsMechanical power

Power measures the rate of work or energy transfer.

ModelPhysicsRigid-body rotational kinetic energy

Rotation stores kinetic energy determined by mass distribution.

ModelPhysicsRolling without slipping

No slip constrains velocity at the contact point.

ModelPhysicsStatic equilibrium and torque balance

Zero net force alone does not prevent rotation.

ModelPhysics · Earth & cosmosYoung, shear and bulk elastic moduli

Stress and strain need a loading geometry and a constitutive range.

ModelPhysicsDensity and fluid pressure

Density is mass per volume; pressure is normal force per area.

ModelPhysicsAbsolute, gauge and differential pressure

A zero gauge reading need not be a vacuum.

ModelPhysicsPascal’s principle and ideal hydraulics

A pressure change is transmitted; pressure need not be equal at different heights.

ModelPhysicsNewtonian viscosity and Poiseuille flow

Viscosity relates shear stress to velocity gradient.

ModelPhysics · ChemistrySurface tension and capillary rise

Interface forces can support pressure jumps and capillary columns.

Model
ModelSource checked

Young, shear and bulk elastic moduli

PhysicsEarth & cosmos

Stress and strain need a loading geometry and a constitutive range.

Key knowledge

For small reversible linear deformations, uniaxial stress σ=F_perp/A gives axial strain ε=ΔL/L₀ with σ=E_Yε. Simple shear obeys τ=Gγ, where γ is the engineering shear strain. Isotropic pressure compression has Δp=−K_BΔV/V₀. The moduli characterize different loading responses and are not interchangeable with strength or fracture limits.

Values and equations

σ=F_perp/A=E_Y(ΔL/L₀); τ=Gγ; Δp=−K_BΔV/V₀

σ,τ,Δp
Axial stress, shear stress and pressure change Pa
E_Y,G,K_B
Young, shear and bulk moduli Pa
F_perp
Signed axial force, positive in tension N
A
Cross-sectional area m²
ΔL,L₀
Length change and initial length m
γ
Engineering shear strain Δx/h 1
ΔV,V₀
Volume change and initial volume m³

Conditions and scope

  • Uniform idealized loading and a valid small-strain linear elastic regime; positive stable moduli. Axial force and stress are signed positive in tension, so compression has negative axial stress and negative length change.
  • The scalar formulas are specified loading limits, not the full tensor constitutive law for anisotropic matter. Engineering shear strain is twice the corresponding small-strain tensor component.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics Volume 1, §12.3: stress strain and elastic modulusSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §12.3 scalar stress/strain relations12.33, axial12.34–12.36, bulk12.39–12.40 and shear12.41–12.43. Avoid the statement that shear-stress concepts never apply to flowing fluids; the record concerns reversible solid elasticity.

2026-10-10 · /root/audit_life_earth_chemistry — independent Chemistry/Life/Earth editor. Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

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Showing 1–3 of 3 relationships

Scientific relationships · 3 / 3

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 1

    Linked statements

    • For small reversible linear deformations, uniaxial stress σ=F_perp/A gives axial strain ε=ΔL/L₀ with σ=E_Yε. Simple shear obeys τ=Gγ, where γ is the engineering shear strain. Isotropic pressure compression has Δp=−K_BΔV/V₀. The moduli characterize different loading responses and are not interchangeable with strength or fracture limits.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

  2. Related to
    Relationship sources · 1

    Linked statements

    • For small reversible linear deformations, uniaxial stress σ=F_perp/A gives axial strain ε=ΔL/L₀ with σ=E_Yε. Simple shear obeys τ=Gγ, where γ is the engineering shear strain. Isotropic pressure compression has Δp=−K_BΔV/V₀. The moduli characterize different loading responses and are not interchangeable with strength or fracture limits.

    This relation concerns the stated young, shear and bulk elastic moduli claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  3. Related to
    Relationship sources · 1

    Linked statements

    • Linear expansion coefficient is α_L=(1/L)(∂L/∂T) under the stated mechanical conditions. For small temperature changes and nearly constant α_L, ΔL≈α_LL₀ΔT. A freely expanding isotropic material has volume coefficient α_V≈3α_L in the small-strain limit. Coefficients can vary with temperature and need not always be positive.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

Entry detailsPermanent link to this entry ↗
Record identity
foundation-physics-linear-elastic-moduli
Revision
foundations-refresh.1
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