Incompressibility Principal Strain Checker
Audit incompressibility through the trace of three principal normal strain rates and report the closure value; no eigenvectors or full tensor are inferred.
Description
Incompressible deformation has zero trace of its strain-rate tensor.
Incompressible deformation has zero trace of its strain-rate tensor. The sum of principal normal rates provides a direct volume-conservation screen.1
Audit incompressibility through the trace of three principal normal strain rates and report the closure value; no eigenvectors or full tensor are inferred.
When to use Incompressibility Principal Strain Checker
Use this for the following task: Audit incompressibility through the trace of three principal normal strain rates and report the closure value; no eigenvectors or full tensor are inferred.
Prepare the measurements and calibration parameters in the declared units. Keep vector entries aligned and choose a consistent spatial frame and time basis.
How to use Incompressibility Principal Strain Checker and understand its results
- Prepare the measurements and calibration parameters in the declared units. Keep vector entries aligned and choose a consistent spatial frame and time basis.
- Enter principalNormalStrainRatesPerYear, closureTolerancePerYear using the field table, then run the tool.
- Read tracePerYear, volumeConservingWithinTolerance, requiredThirdPrincipalStrainPerYear. Interpret flags, units, ordering and placeholder values using the rules below.
- Review any reported issue or failed check, correct the supplied values when appropriate, and verify the result in its intended context.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| principalNormalStrainRatesPerYear | Principal normal strain rates per year | list of number; each entry: number | Required |
| closureTolerancePerYear | Closure tolerance per year | number | Required |
Supply exactly three principal normal rates and a nonnegative tolerance. Test the absolute trace inclusively and return the third rate needed to close the first two.2
trace = ε̇1+ε̇2+ε̇3; required third = −ε̇1−ε̇2 This summarizes the declared operation. Units, indexing, inclusivity and exceptional cases are explained in the surrounding text.
| Output field | Meaning | Value type |
|---|---|---|
| tracePerYear | Trace per year | number |
| volumeConservingWithinTolerance | Volume conserving within tolerance | boolean |
| requiredThirdPrincipalStrainPerYear | Required third principal strain per year | number |
{
"input": {
"principalNormalStrainRatesPerYear": [
0.1,
0.2,
-0.31
],
"closureTolerancePerYear": 0.005
},
"output": {
"tracePerYear": -0.009999999999999953,
"volumeConservingWithinTolerance": false,
"requiredThirdPrincipalStrainPerYear": -0.30000000000000004
}
}Limitations and assumptions
This does not infer eigenvectors, shear components or density changes.
Constants and empirical coefficients are supplied rather than calibrated. Check units and observational applicability before interpreting the model. Malformed requests produce input errors. A successfully evaluated request can still contain false flags, empty result lists or a result outside the supplied threshold; those outcomes have the meanings stated above.
Alternative or Complementary methods
Choose Longitudinal Strain Rate for this operation: Estimate interval longitudinal normal strain rate from velocity gradients along a supplied flow transect; not transverse or tensor shear strain. For a complementary task, use Strain Heating Contribution for this operation: Contract full symmetric stress and strain-rate tensors, counting off-diagonal shear twice; negative power is preserved and flagged as inconsistent with positive dissipation, not relabeled heating.
Further background: Ice rheology.
References
-
Ice rheology — PISM
Similar or alternative tools
- Longitudinal Strain Rate
Estimate interval longitudinal normal strain rate from velocity gradients along a supplied flow transect; not transverse or tensor shear strain.
- Strain Heating Contribution
Contract full symmetric stress and strain-rate tensors, counting off-diagonal shear twice; negative power is preserved and flagged as inconsistent with positive dissipation, not relabeled heating.