Give it time to rearrange: sources & model

Make the same small move at different speeds, park a material-testing carriage, and watch its force change. Explore polymer networks, relaxation, creep and real research images without inventing a breaking rule.

What supports the explanation?

What this model assumes

1. The original testing bench uses ideal uniform simple shear. It does not recreate the paper’s cone-plate force measurement or the separate optical fixture.
2. Quantitative strain stays within ±1%. Large-amplitude source images are separate observations, not settings for the linear solver.
3. The model is linear, homogeneous, isothermal and single-mode. It omits gravity sag, necking, drying, slip, inertia, chemistry, chain scission and fracture.
4. Calculated transient responses are not observed pull measurements. Fast ideal comparisons can contain frequencies outside the measured sweep.
5. The network lens is schematic. It does not track atoms, measure bond counts or turn τ into a universal junction lifetime.
6. PVA–borate slime, controlled Tetra-PEG, permanently crosslinked materials and cornstarch suspensions are not interchangeable specimens.
7. Video and replay alter observation time, not material temperature or relaxation parameters. Source photos remain six discrete states, not invented footage.
8. The paper activity makes no material-property measurement. Optional prepared-material observation requires an age-appropriate product, its instructions and adult supervision; no mixing or deliberate rupture is needed.
9. A specific research specimen: The numerical anchor is Sato et al.’s 20 kg/mol, 60 g/L Tetra-PEG network at 25°C. Their reported Maxwell fit gives G = 4800 Pa and τ = 0.39 s. These are rounded fit parameters, not universal polymer constants.
10. What was measured and what we calculate: The reported small-amplitude oscillatory sweep used strain amplitude 0.01 and angular frequency 0.01–10 rad/s. Our controlled ramps, holds and releases are model-derived transients using that fit; they are not measured pull traces from the paper.
11. A series constitutive model: The Maxwell model has γ = γ_elastic + γ_viscous, σ = Gγ_elastic and dγ_viscous/dt = σ/η, with η = Gτ = 1872 Pa·s. The spring and dashpot are constitutive analogies, not literal pieces inside slime.
12. Exact evolution over a controlled move: For constant strain rate v during Δt, σ_next = σ_previous exp(−Δt/τ) + Gvτ[1 − exp(−Δt/τ)]. Signed stress is retained through reversals. Fixed-position holds set v to zero; stress then decays exponentially.
13. A relaxation time is not complete relaxation: After one τ at fixed strain, the remaining ideal stress is exp(−1), about 36.8% of its starting value. It is not zero. A macroscopic network relaxation time is also not automatically one junction’s bond lifetime.
14. Creep and residual deformation: For constant stress σ₀, γ(t) = σ₀/G + σ₀t/η. At zero-load release, the ideal elastic term recovers and the viscous term remains. With 12 Pa held for 0.39 s, strain approaches 0.005 before release and becomes 0.0025 afterward.
15. Geometry and magnification: The original uniform teaching cassette assumes area 1 cm² and gap 2 mm. Force = stress × area; displacement = strain × gap. A 1% shear is 20 µm sideways, and an ideal 48 Pa step corresponds to 0.0048 N. Enlarging motion on screen does not change these values.
16. Storage and loss under oscillation: For x = ωτ, G′ = Gx²/(1+x²) and G″ = Gx/(1+x²). Both equal G/2 at x = 1, where the loss modulus peaks. Angular frequency ω is in rad/s; ordinary frequency is ω/(2π) Hz.
17. Different time ratios answer different questions: τ divided by an experiment duration compares relaxation and imposed time scales. Strain rate multiplied by τ is a different dimensionless quantity. Neither is a probability of snapping or a universal breaking deadline.
18. One Maxwell mode has limits: This model can flow indefinitely under sustained load, unlike an ideal network with permanent equilibrium elasticity. Real polymer materials can require distributions of relaxation times, additional elastic contributions or nonlinear models.
19. Shear thickening is not every resistance to fast motion: An increased transient force during a quicker imposed deformation is not itself a steady shear-thickening measurement. Concentrated particle suspensions and temporary polymer networks can resist motion through different mechanisms.
20. Optical observations have their own meaning: Sato Figure 5 maps optical retardation in nanometers and accompanying brightness under six large strain amplitudes. The paper distinguishes nonlinear response from detected spatial heterogeneity. These images are not molecular pictures, temperature maps or observations inside our small-strain solver.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Original simple-shear material-testing bench with a transparent sample cassette and magnified plate movement. Not manufacturer CAD, measured molecular geometry or a fracture animation.