Inspect the loop.
Keep its meaning.

Bring the recorded history

One UTF-8 numeric CSV, up to 20,000 source rows. No data are preloaded, sorted, deduplicated, smoothed or repaired.

Review the chosen cycles

Inspect upward-zero candidates or enter exact source-row bounds. Missing readings and declared time gaps cannot be bridged.

Read defined quantities

Separate signed work, accepted-loop work magnitude, displacement-extrema stiffness, force asymmetry and unloading zero-force intercepts.

Keep a reproducible record

Save the exact source text and recipe locally, then export full metrics, a report, an SVG trace and stable calculation snapshots for manuscript checks.

Cycle completeness

Candidates use successive upward displacement-zero crossings. Boundary force is linearly interpolated only within adjacent valid source records. A cycle must be reviewed, contain at least five boundary/recorded points, two displacement reversals, both force signs and both displacement directions above the entered minimum amplitude.

Endpoint displacement and force differences must both lie within the researcher’s declared absolute closure tolerances. Missing readings, nonincreasing time or an excessive adjacent time gap split the trace; incomplete ranges have no cycle metrics.

Signed and magnitude work

W = Σ ½(Fᵢ + Fᵢ₊₁)(uᵢ₊₁ − uᵢ), in kN·mm = J. Accepted-loop work magnitude is |W|, rather than the sum of absolute incremental work. Source order and force/displacement polarity determine its sign.

No artificial closing segment is integrated. Endpoint mismatch is reported beside the chosen tolerances. This is a near-closed-loop work descriptor; offsets, inertia and rate effects can prevent interpretation as physical energy dissipation.

Stiffness and comparison

K = (force at maximum displacement − force at minimum displacement)/(maximum displacement − minimum displacement). Tied extrema use their first source occurrence. A nonpositive or degenerate chord is unavailable. This chord is not a force-extrema effective stiffness formula.

K/Kref requires an accepted reference with positive K, declared comparable conditions and both directional amplitudes within the selected relative tolerance. The amplitude check does not establish comparable loading rate, specimen or measurement conditions by itself.

Direction and unloading

Directional force extrema are reported independently from displacement extrema. Force asymmetry is positive maximum force divided by the absolute negative minimum force.

For each direction, the unloading intercept is the last zero-force crossing after that direction’s displacement extreme and before displacement enters the opposite sign. Choose recorded exact zero readings or linear bracketing interpolation. Missing crossings stay unavailable; these are unloading intercepts, rather than permanent residual deformation.