The following paper may be helpful for you, even though I do not know the experimental configuration of your tests:

Article Study on constitutive model of structural steel under cyclic loading

Thank you, Arti Yadav

I am focusing on modeling. and I want to use the built-in model inside Abaqus without the need to use UMAT sub-routine as done in the paper you shared.

thanks.

Mohamed Abdelhameed You can find some information about low-cycle fatigue including video training and software files in the following link:

https://caeassistant.com/product/simulation-of-fatigue-in-abaqus/

Thanks a lot, Alvin Molberg

actually, there are two methods to simulate progressive damage resulting from law cyclic fatigue in Abaqus:

1- based on linear fracture mechanics using Paris law.

2- based on continuum damage mechanics, The damage initiation and evolution are characterized by the stabilized accumulated inelastic hysteresis strain energy per cycle.

the practice you shared is the first method, and I need to use the second method

thank you for your effort Alvin Molberg

Actually, I found how to implement the low cyclic fatigue continuum damage model which is built in Abaqus. the steps are the following:

1- define the inelastic material behavior

2- define the cyclic load using the direct cyclic step [the model work only with the direct cyclic step]

3- set the damage initiation criterion to HYSTERESIS ENERGY [it is not available in GUI - you have to write it in the input file]

4- write the two parameters C1 and C2 in the input file [you can find them in this article (10.1109/ECTC.2000.853299)]

5- set the damage evolution criterion to HYSTERESIS ENERGY [also not available in the GUI - write it in the input file ]

6- write the two parameters C3 and C4 in the input file [fine them in the same above paper].

Make sure to plastic deformation in each cycle to initiate damage.

done

@ Mohamed Abdelhameed,

Thank you very much for your answer. Please can you tell me which output variable in abqus corresponds to the inelastic energy that we need to consider in your proposed model.

This energy you use in the damage initiation

Thank you

Mohamed Abdelhameed Hi Mohamed thanks for your info, have you found out how to obtain the HYSTERESIS ENERGY damage initiation and evolution material constants?

I found the following pages introducing the HYSTERESIS ENERGY damage initiation and evolution model with ABAQUS, but no info about how to obtain the related material constants (c1, c2, c3, c4):

https://abaqus-docs.mit.edu/2017/English/SIMACAEMATRefMap/simamat-c-damageinitfatigue.htm

https://abaqus-docs.mit.edu/2017/English/SIMACAEMATRefMap/simamat-c-damageevolfatigue.htm