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PINCHING4 Uniaxial Material Model Discussion
The example files (RCyclicPinch.tcl, procUniaxialPinching.tcl, procRCycDAns.tcl) create a one-dimensional structural model consisting of a single truss element of length 1.0 and area 1.0 (Figure 1). The Pinching4 uniaxial material model is used to simulate the stress-strain response of the truss material. The truss is subjected to a pseudo-static cyclic loading. Several files are provided that include different input parameters for the Pinching4 material model and result in different load-displacement histories for the truss structure. Refer to the documentation about the Pinching4 uniaxial material model for additional information.
Input for the Pinching4 Uniaxial Material Model
Refer to the documentation of the Pinching4 uniaxial material model for an explanation of the following notation.
Response Envelopes:
In these examples the pinching material model is demonstrated with two different load-deformation response envelopes. Envelope 1 (Figure 2) defines a hardening-type response while Envelope 2 (Figure 2) defines a softening-type response.
Envelope 1 (Figure 2):
Envelope 2 (Figure 2):
Load-Unload Response Parameters:
The form of the load-unload response, and the extent of pinching in the response history, is defined by the following six parameters. In each of the examples, the following values are used.
Strength and Stiffness Degradation Parameters:
The Pinching4 uniaxial material model simulates degradation of stiffness and strength under cyclic loading. The example files demonstrate, individually and in combination, each of the two stiffness degradation options and the one strength degradation option. The following parameters are used to define strength and stiffness degradation, as needed, in the example files.
Tcl Scripts:
The following tcl script files are used to run the examples:
Lines should be commented out as necessary within RCyclicPinch.tcl to exercise different degradation models of the Pinching4 uniaxial material model and different load histories.
If the structure is subjected to a monotonic load history, the load-displacement history is shown in Figure 2 results with the actual response history depending on the envelope chosen for the material model. If the structure is subjected to a cyclic load history (Figure 3), one of the load-displacement histories shown in Figure 4 results, with the exact response depending on the strength and stiffness degradation model employed. In this case the damage type activated was "Energy". The case in which the damage type activated was "Cycle" is shown in Figure 5.
Figures:
Figure 1: Structural Model
Figure 2: Response Envelopes
Figure 3: Cyclic Displacement History
Figure 4: Load-Deformation Response Histories ("Energy type damage")
Figure 5. Plot showing Both Stiffness and Strength Degradation for Damage Type "Energy" and "Cycle"