Deformation Rate Glen N Exponent

Fit n and apparent A from positive stress/strain observations in log space; fitted A absorbs enhancement and calibration, unlike a forward Glen-law prediction.

Description

A power rheology becomes linear after taking logarithms of stress and strain rate.

A power rheology becomes linear after taking logarithms of stress and strain rate. Its slope estimates the apparent stress exponent.^[1]

Fit n and apparent A from positive stress/strain observations in log space; fitted A absorbs enhancement and calibration, unlike a forward Glen-law prediction.

When to use Deformation Rate Glen N Exponent

Use this for the following task: Fit n and apparent A from positive stress/strain observations in log space; fitted A absorbs enhancement and calibration, unlike a forward Glen-law prediction.

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 Deformation Rate Glen N Exponent 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 positiveStressPa, positiveStrainRatesPerYear using the field table, then run the tool.
Read fittedGlenExponent, fittedRateFactor, logFitRSquared. 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
positiveStressPa	Positive stress pa	list of number; each entry: number	Required
positiveStrainRatesPerYear	Positive strain rates per year	list of number; each entry: number	Required

Fit aligned positive observations in log space by least squares. Return a positive fitted exponent, exponentiated intercept and log-space R squared.^[2]

ln(strainRate) = ln(A) + n ln(stress)

This summarizes the declared operation. Units, indexing, inclusivity and exceptional cases are explained in the surrounding text.

Output field	Meaning	Value type
fittedGlenExponent	Fitted glen exponent	number
fittedRateFactor	Fitted rate factor	number
logFitRSquared	Log fit r squared	number

json

{
  "input": {
    "positiveStressPa": [
      1,
      2,
      4
    ],
    "positiveStrainRatesPerYear": [
      0.1,
      0.8,
      6.4
    ]
  },
  "output": {
    "fittedGlenExponent": 2.9999999999999996,
    "fittedRateFactor": 0.10000000000000002,
    "logFitRSquared": 1
  }
}

Limitations and assumptions

Apparent A absorbs enhancement and calibration. This is an empirical fit without uncertainty intervals or separation of temperature effects.

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 Glen Flow Law Strain Rate for this operation: Evaluate signed scalar Glen shear strain rate A·E·sign(tau)|tau|^n; A units follow n, and shear tensor strain rate differs by a factor two from engineering shear rate. 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
Deformation Rate Glen N Exponent — tool.io

Similar or alternative tools

Glen Flow Law Strain Rate
Evaluate signed scalar Glen shear strain rate A·E·sign(tau)|tau|^n; A units follow n, and shear tensor strain rate differs by a factor two from engineering shear rate.
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.