Dear Johnny,

Sigma is the stress for which the stress-strain curve starts to deviate from the elastic behaviour.

Firstly, I think, that You will find this paper very interesting:

https://www.researchgate.net/publication/228525599_Identification_of_parameters_of_concrete_damage_plasticity_constitutive_model

and maby this:

https://www.researchgate.net/publication/288989106_Analiza_numeryczna_plyty_stropu_zespolonego_stalowo-betonowego_w_sasiedztwie_wezla_podatnego

Secondly, please find in the attachment an excel spreadsheet with discrete functions from Jankowiak&Lodygowski implemented.

Best Regards,

Bartosz Grzeszykowski

Article Identification of parameters of concrete damage plasticity c...

Chapter Analiza numeryczna płyty stropu zespolonego stalowo-betonowe...

Dear Johnny,

In order to define dt and dc damage parameters, all You need to have is a full Sigma-Epsilon curve from uniaxial compression test and tensile properties - it can be experimental or You can use known in the literature constitutive relations.

Next, the damage parameters can for example be defined as follows (c - compression, t-tension):

d_c(Sigma_c,Epsilon_c) =  0,  for Epsilon_c Epsilon_cm

d_t(Sigma_t,Epsilon_t) =  0,  for Epsilon_t Epsilon_tm

Epsilon_cm / Epsilon_tm = strain of concrete at the peak stress in compression (fcm) / tension (ftm)

You can also use other formulas or modify the above using some coefficients, for example there is some degradation of concrete stifness before the peak stress - the above formula does take in into account. It is crucial to perform a parametric analysis regarding this issue.

Best Regards,

Bartosz Grzeszykowski

Dear bartosz,

Thanks for your input, I am aware of calculating damage variables, my concern is that I do not have experimental data and would like to use some empirical cocnrete stress-strain curve (Like Mander concrete model) to get these damage variables. The problem is that concrete model such as Mander is not very good for defining damage variables since the value of damage variables falls below 1 ( usually in range of 0.6-0.8).

I'm looking to see if there are other cocnrete models in the literature that can fairly give  damage variables (at least up to 0.9). 

Cheers, 

Dear Johnny,

To produce damage parameteres dc and dt equal to 1,0, stress in the post-peak must reach 0. Every stress-strain model for concrete described by continuous function will be assymptotic to 0, therefore You will never reach damage parameters equal to 1,0.

You can always use some piecewise functions.

Best Regards,

Bartosz Grzeszykowski

Hi Bartosz,

Thanks for your reply. I agree with that point, but there are some empirical models such as Hsue or Hordijk that give fairly close to full damage state. I was wondering if others are familiar with other cocnrete models. 

Cheers, 

Hi again,

to check the accuracy of cracking strain values to ensure that they're in descending order, the following formula is used by abaqus:

cracking strain = total strain -( Sigma/E0)

Is total strain the strain at the end of the curve? Also sigma is the tensile stress after post peak or is the peak tensile stress. Then cracking strain is used to calculate plastic strain as below:

Plastic strain = cracking strain - (dt/1-dt * Sigma/E0)

I am following this and not getting any negative or descending values but the error says the tension damage input is incorrect. Here are my values:

dt: 

0

0.537873051666752

0.739309335604404

0.818420353800213

0.864910150102302

0.903945397887620

0.938509480089892

0.967254152746396

0.989597008096301

yield strain:

0

2.50000000000000e-05

5.00000000000000e-05

7.50000000000000e-05

0.000100000000000000

0.000125000000000000

0.000150000000000000

0.000175000000000000

0.000200000000000000

yield stress:

3394112.55000000

1568510.87500000

884813.456000000

616301.756000000

458510.155000000

326020.130000000

208705.745000000

111143.091000000

35308.9250000000

E is 25 GPa

Dear Johnny,

Sigma is the stress for which the stress-strain curve starts to deviate from the elastic behaviour.

Firstly, I think, that You will find this paper very interesting:

https://www.researchgate.net/publication/228525599_Identification_of_parameters_of_concrete_damage_plasticity_constitutive_model

and maby this:

https://www.researchgate.net/publication/288989106_Analiza_numeryczna_plyty_stropu_zespolonego_stalowo-betonowego_w_sasiedztwie_wezla_podatnego

Secondly, please find in the attachment an excel spreadsheet with discrete functions from Jankowiak&Lodygowski implemented.

Best Regards,

Bartosz Grzeszykowski

Article Identification of parameters of concrete damage plasticity c...

Chapter Analiza numeryczna płyty stropu zespolonego stalowo-betonowe...

Dear Bartosz,

Thanks for the attachments. Are the data in the excel sheet from experiments? 

Dear Johnny,

The data in excel sheet is from Jankowiak&Lodygowski's paper. Fig. 1 and 2 caption:

Uniaxial compression test of concrete, class B50 – experimental curve

(Home Institute)

Best Regards,

Bartosz Grzeszykowski

Dear Johnny,

Below are two papers where you can find data at elevated temperatures and 20°C. Bear in mind that concrete is not a generic material, for example in the given reference no coarse aggregate was used.

Suitability of the damage-plasticity modelling concept for concrete at elevated temperatures: Experimental validation with uniaxial cyclic compression tests by Neuenschwander, Knobloch and Fontana. DOI: 10.1016/j.cemconres.2015.07.013

and/or

Generic Model Stress-Strain Relationship for Concrete in Compression at Elevated Temperatures by Neuenschwander, Knobloch and Fontana. DOI: 10.14359/51689468

Regards,

Wojciech