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Sandbox Physics

M027 · Solid mechanics

Stress–Strain Material Tester

Run a tensile hold, unload, reverse and return protocol on elastic, plastic, brittle or viscoelastic specimens. Track internal state and the energy ledger; recover a loading slope from acquired force and gauge extension.

Interactive modelStress–Strain Material Tester
Selected protocol timeReady\text{Ready}
Engineering strainReady\text{Ready}
Engineering stressReady\text{Ready}
Signed tensile forceReady\text{Ready}
Permanent plastic strainReady\text{Ready}
Stored recoverable and hardening energyReady\text{Ready}
Signed external workReady\text{Ready}
Dissipated or fracture-loss energyReady\text{Ready}
Work–energy closureReady\text{Ready}
Virgin loading slope from raw recordReady\text{Ready}
Acquired stationsReady\text{Ready}
Model stateReady\text{Ready}

Physics tutorial

History inside a material

BackgroundA shared axial loading frame connects physical geometry, a constitutive or stability model, and separately acquired observations.

Why it mattersUse loading, unloading and controlled geometry to distinguish competing explanations.

Start with the essentials

Focus question
Does zero extension mean no stored stress?
One-sentence intuition
Follow the same physical state through apparatus, readouts and the energy or stability record.

Core mathematical model

Engineering observables

ε=ΔLL0σ=FA0\begin{aligned}\varepsilon&=\frac{\Delta L}{L_0}\\\sigma&=\frac{F}{A_0}\end{aligned}

Use original geometry. Neither true stress nor a changing neck area is inferred.

Isotropic plasticity

σ=E(ε−εp)∣σ∣≤σy+Hαdα=∣dεp∣\begin{aligned}\sigma&=E(\varepsilon-\varepsilon_p)\\|\sigma|&\leq\sigma_y+H\alpha\\d\alpha&=|d\varepsilon_p|\end{aligned}

Permanent strain changes sign with plastic flow; accumulated plastic strain and the yield radius only increase.

One Maxwell arm

σ=E∞ε+zz˙+zτ=(E0−E∞)ε˙\begin{aligned}\sigma&=E_\infty\varepsilon+z\\\dot z+\frac{z}{\tau}&=(E_0-E_\infty)\dot\varepsilon\end{aligned}

The transient spring stress relaxes during a hold. Exact constant-rate updates avoid a stiff time-step artifact.

Mechanical energy ledger

W=V0∫σ dεW=Ψ+D\begin{aligned}W&=V_0\int\sigma\,d\varepsilon\\W&=\Psi+D\end{aligned}

Track signed external work, recoverable and hardening storage, and irreversible dissipation. Brittle release enters loss.

Raw loading slope

FiA0≃c+E^ΔLiL00<ΔLiL0≤3×10−4\begin{aligned}\frac{F_i}{A_0}&\simeq c+\widehat E\frac{\Delta L_i}{L_0}\\0&<\frac{\Delta L_i}{L_0}\leq3\times10^{-4}\end{aligned}

Only virgin tensile-ramp observations and original geometry enter. A viscoelastic slope depends on the loading rate.

Common difficulties

Model boundary

Typical misconceptionA smooth rendered curve proves physical validity.

Better mental modelUse explicit domain checks and acquired records; the teaching laws do not certify real specimens.

Run the experiment

  1. 01

    Unload after yielding

    Choose Yield and unload; scrub through the full protocol.

    What to observe: Zero total strain can require a nonzero stress because permanent strain remains.
  2. 02

    Hold extension fixed

    Choose Viscoelastic hold; vary hold duration and ramp rate.

    What to observe: Stress relaxes during fixed extension; the equilibrium spring keeps a residual tensile load.
  3. 03

    Book released energy

    Choose Brittle rupture and inspect the energy row before and after the threshold.

    What to observe: The teaching cutoff is irreversible; released storage enters loss rather than disappearing from the ledger.
  4. 04

    Recover a loading slope

    Acquire the full protocol, inspect raw channels, export CSV and change noise.

    What to observe: The virgin fit uses raw force and extension; viscoelasticity changes its apparent slope with rate.