OGS
[case] Sigmoid

Sigmoid property with configurable independent variable

The sigmoid function is a smooth step function with a configurable range defined by the following formula

\[ (X_\mathrm{u} - X_\mathrm{l}) \left[1 + \exp(-k(X - X_\mathrm{c})) \right]^{-1} + X_\mathrm{l} \]

where

  • \(X_\mathrm{l}\) is the lower bound (value as X -> -inf)
  • \(X_\mathrm{u}\) is the upper bound (value as X -> +inf)
  • \(X\) is the independent material variable (temperature, pressure, etc.)
  • \(X_\mathrm{c}\) is the midpoint (a.k.a. inflection point) of the transition
  • \(k\) controls the steepness of the transition; a positive \(k\) gives a monotonically increasing curve, a negative \(k\) a decreasing one.

Child parameters, attributes and cases

Additional info

No additional info.

Used in the following test data files