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.

Description

Strain power contracts stress with deformation rate.

Strain power contracts stress with deformation rate. For symmetric tensors, off-diagonal shear components occur twice in the full contraction.^[1]

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.

When to use Strain Heating Contribution

Use this for the following task: 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.

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 Strain Heating Contribution 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 stressTensorPa, strainRateTensorPerYear, secondsPerYear using the field table, then run the tool.
Read signedVolumetricStrainPowerWattsPerM3, nonnegativeDissipationScreen. 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
stressTensorPa	Stress tensor pa	list of list of number; each entry: list of number; each entry: number	Required
strainRateTensorPerYear	Strain rate tensor per year	list of list of number; each entry: list of number; each entry: number	Required
secondsPerYear	Seconds per year	number	Required

Supply two exactly symmetric 3×3 tensors using tensor shear rates per year. Multiply corresponding components and sum; preserve negative power and report whether it is nonnegative.^[2]

power_W/m³ = ΣiΣj σij ε̇ij / secondsPerYear

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

Output field	Meaning	Value type
signedVolumetricStrainPowerWattsPerM3	Signed volumetric strain power watts per m3	number
nonnegativeDissipationScreen	Nonnegative dissipation screen	boolean

json

{
  "input": {
    "stressTensorPa": [
      [
        2,
        1,
        0
      ],
      [
        1,
        3,
        0
      ],
      [
        0,
        0,
        4
      ]
    ],
    "strainRateTensorPerYear": [
      [
        1,
        2,
        0
      ],
      [
        2,
        1,
        0
      ],
      [
        0,
        0,
        -2
      ]
    ],
    "secondsPerYear": 10
  },
  "output": {
    "signedVolumetricStrainPowerWattsPerM3": 0.1,
    "nonnegativeDissipationScreen": true
  }
}

Limitations and assumptions

Engineering shear rates differ by a factor of two. A negative result is not relabeled as heating and can indicate inconsistent supplied components.

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 Friction Heating Melt Contribution for this operation: Balance basal traction×sliding power and caller heat partition to ice melt at pressure melting; not geothermal heating or a sliding-speed prediction.

Further background: Ice rheology.

References

Ice rheology — PISM
Strain Heating Contribution — 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.
Friction Heating Melt Contribution
Balance basal traction×sliding power and caller heat partition to ice melt at pressure melting; not geothermal heating or a sliding-speed prediction.