3.1.5.25. Fatigue Material Wrapper

This command is used to construct a Fatigue uniaxial material wrapper. The wrapper uses a modified rainflow cycle-counting algorithm to accumulate damage in the wrapped material using Miner’s rule, based on Coffin-Manson log-log relationships for low-cycle fatigue. It does not change the stress-strain (or force-deformation) response of the wrapped material until fatigue life is exhausted; then the wrapper returns zero stress and zero tangent.

uniaxialMaterial Fatigue $matTag $otherTag <-E0 $e0> <-m $m> <-min $epsmin> <-max $epsmax>

Argument	Type	Description
$matTag	integer	unique material tag
$otherTag	integer	tag of a previously-defined UniaxialMaterial
$e0	float	(optional) strain at which one cycle causes failure; default 0.191
$m	float	(optional) slope of Coffin-Manson curve in log-log space; default -0.458
$epsmin	float	(optional) global minimum strain/deformation for failure; default -1e16
$epsmax	float	(optional) global maximum strain/deformation for failure; default 1e16

3.1.5.25.1. Description

The model accounts for low-cycle fatigue. A modified rainflow cycle counter tracks strain amplitudes and is used with a linear strain-accumulation model (Miner’s rule) and Coffin-Manson relationships. When the damage level reaches 1.0, the force (or stress) of the wrapped material is set to zero (numerically 1e-8). If failure is triggered in compression, the stress is dropped at the next zero-force crossing. The material treats each point as the last point of the history for damage tracking; if failure is not triggered, that pseudo-peak is discarded. Failure can also be triggered by exceeding the optional minimum or maximum strain limits (defaults are very large so that only fatigue controls). The default E0 and m are calibrated from low-cycle fatigue tests on European steel sections (Ballio and Castiglioni 1995); see Uriz (2005) for calibration details.

Valid recorder responses for the wrapped material are stress, tangent, strain, stressStrain, and damage. The stress, strain, and tangent options must be supported by the wrapped material.

3.1.5.25.2. Damage recorder

To record fatigue damage, use the element recorder with the damage response.

Fiber section elements: The argument after material (or fiber) is the fiber index, not the material tag. Using material or fiber gives the same result. To target a fiber by coordinates, add one more argument after fiber (y and z, or the appropriate coordinate).

Truss elements: Use material without a tag after it. Adding a material tag after material will not work.

Tcl Code

# Fiber section: record damage of 1st fiber (index 0) — "material" and "fiber" equivalent
recorder Element -xml Damage1.out -time -ele 1 2 section 1 material 0 damage
recorder Element -xml Damage2.out -time -ele 1 2 section 1 fiber 0 damage

# Fiber section: record damage of fiber near center by coordinates
recorder Element -xml Damage3.out -time -ele 1 2 section 1 fiber 0.1 0.1 damage

# Truss: use "material" with no tag
recorder Element -file Damage4.out -time -ele 1 material damage

Python Code

# Fiber section: record damage of 1st fiber
ops.recorder('Element', '-xml', 'Damage1.out', '-time', '-ele', 1, 2, 'section', 1, 'material', 0, 'damage')

# Truss: use "material" with no tag
ops.recorder('Element', '-file', 'Damage4.out', '-time', '-ele', 1, 'material', 'damage')

Note

For theory and implementation details see Uriz (2005) and the OpenSees wiki.

3.1.5.25.3. References

Uriz, P. (2005). “Towards Earthquake Resistant Design of Concentrically Braced Steel Structures,” Ph.D. Dissertation, UC Berkeley.
Ballio, G., and Castiglioni, C. A. (1995). “A Unified Approach for the Design of Steel Structures under Low and/or High Cycle Fatigue.” Journal of Constructional Steel Research, 34, 75-101.

Code developed by: Patxi Uriz, Exponent; modifications by Kevin Mackie.