Concrete simulation

FERNANDO

Is it possible to consider a compression-only material with a non-linear stress-strain curve? It would be very useful for concrete.

disla

Hi Fernando and welcome,

Ccx manual says that for those models “In essence, a one-dimensional Hooke-type relationship is established between the principal stresses and principal strains.” So, the Only tension and Only compression materials models implemented basically behave as linear under Tension/Compression respectively and can sustain up to a given pressure/tension in the opposite direction respectively.
I have attached a quick example file.






Don’t pay too much attention to Dimensions and Numbers. They probably don’t make too much sense. Only-compression is set up by means of custom cards and ccx solver.
This material models are prone to give convergence issues close to the BC. Try to avoid any peak stress specially in tension and provide some allowance in tension to start .
You can also check the file concretebeam.inp provided with the ccx test examples:

You can call many other material behaviors installing MFRONT libraries (e.g Modified Mohr Coulomb, Drucker Prager w/o Cap, Mazars, unilateral -Mazars). There have been some attempts on the forum but you better ask in the ccx forum directly as it is very specific.

MikeMcMullen

I have had some luck. There is an approximation for the tensile strength that works ok for matching bending tests of cracked reinforced concrete that uses a tensile strength of about 0.30mpa to 0.60 mpa or so and nominal reinforcing of perhaps 0.18%. The idea is that the concrete tension falls from a peak of 0.35 mpa at low strain to near 0.01 mpa at the yield strain of rebar as the steel tension/concrete area increases to perhaps 0.75 mpa.
Note the modulus of rupture is 3.5 mpa-ish so I run with ultimate loads with a tensile strenght of 3.5 mpa to see if there is significant cracking, then if there is, run again with the concrete tension capacity set to .3mpa-.6mpa. If the strength is inadequate I increase the concrete tension till it works and use minimum steel to match the tensile strength of the concrete at failure. Not precise, but nothing is with concrete.
Alternatively your steel can be added as a grid sharing nodes and with a representative steel stress strain model and the concrete as above. Convergence of solutions can be slow when any concrete stresses exceed its tensile strength, likewise if the concrete exceeds its tensile strength and the steel exceeds its yield and does not have a significant non-negative slope after yield. Some problems one thinks would be problematic are not if geometric non-linearity is used as there sometimes may be significant internal arching reducing tensions. (for safety best to reduce youngs modulus to reflect shrinkage restraint and potential deterioration).

FERNANDO

Thank you very much for the responses disla and MikeMcMullen. It is clear that the tension-only and compression-only models are linear.
I would like to find the best material model available in CCX to simulate the behavior of concrete, maybe it is just linear compression.
Two questions arise:
-I do not have the PARDISO solver, I do not know its advantages or how to install it.
-How can I install the MFRONT libraries

FERNANDO

I just installed the mkl pardiso library and it works. I assume that this option allows using multiple processors

disla

I assume that this option allows using multiple processors

For running multprocessor, create new Windows System Variables with settings:

OMP_NUM_THREADS=6
CCX_NPROC_STIFFNESS=6

Using more than 6-8 proc for most models will not reduce run time further.

Then check in your ccx monitor when running an analisys. It should show the number of processors being used.

There is a post for you to compare your system performance .

https://mecway.com/forum/discussion/836/mecway-pc-benchmarks/p1

Sergio

I found today this nice paper about reinforced concrete, maybe could be redone in Mecway/Calculix


https://www.linkedin.com/posts/aymanelfouly_els-software-progressive-collapse-validation-activity-7148028782396719104-3Dno?utm_source=share&utm_medium=member_desktop

MikeMcMullen

Calculix 2.21 now includes Mohr Coulomb. What we need is a good reinforced concrete example using it. It would still not include the specific non-linearity of concrete in tension and compression, but may be good enough. Some mentions from past implementations in calculix indicated it was fast and converged well. I have not taken the time to read the Calculix manual on this.

disla

I'm not civil engineer and don't have experience with concrete, but if anyone else is up for it, I'm in. I can try to apply this Mohr Coulomb to my previous file as I know is converging fast.

Later we could try;

1.2. Reinforced Concrete Beam or
1.3. Reinforced Concrete Slab.

Seem good candidates to start.

FERNANDO

That sounds good. The Mohr-Coulomb model for civil engineering is interesting. Also for geotechnics.

disla

Now I have remembered I already
made a test example with Mohr Coulomb but it is related to Soil Stability.
It is a copy paste based on a You tube video and I did not found too much application to my working area so I didn't go more in deep.

FERNANDO

It is an interesting example to apply the Mohr-Coulomb model. By obtaining the appropriate parameters it can be applied to soils and concrete.

disla

Hi Fernando,

Do you have some realistic parameters for a standard concrete.? Let's Say HM-25
I can't find information about :




**• Dilation angle ψ in degrees and the relationsheep between
**• Cohesion yield stress and its Equivalent plastic strain asociated.

Must be some kind of Stress(Cohesion Yield)-Strain curve Isn't it.

FERNANDO

For an HA-25 I would use these values:
Dessity: 23 Kn/m3
Friction angle: 35º
Cohesion: 650 Kn/m2

FERNANDO

Modulus of elasticity: 272640 Kp/cm2

FERNANDO

Indeed the relationship between cohesion and strain is a model with hardening.

MikeMcMullen

Ooh. That would be wonderful. Especially if it worked with Mecway. If I read the manual right it only requires a few more cards than the compression only approach, and a knowlege of the friction angle and dilation angle. There are a few examples in Free Cad that can give plausible values of these. Looking up research guesses for medium strength normal density concretes I get ~37 deg friction angle (20-55 deg), 0.1 F'c (.08 F'c-.25 F'c) peak tensile strength, quite a bit less mean tensile resistance, and dilatancy angle of perhaps 5-25 deg., 5 deg being highly confined and 25 relatively unconfined, with low density concrete perhaps -5 deg. Cube compresssion strength, cylinder compression strength, and split cylinder tests are run and data is readily available (sometimes with strain data), and FEM examples of them would allow checking the fit and plausibility of the parameters used. Other members of this group may have better ideas as structural engineers seldom use this approach for design and these parameters are not easily measured.
Note the Mohr circle approach is much more commonly used by structural engineers for soil stability problems, but there is no reason not to use it for concrete, lacking better methods.
https://upcommons.upc.edu/bitstream/handle/2117/131799/24026948.pdf may provide some info, but it does not narrow the likely parameters much. Fernando's suggested value are similar to what I have seen for low to medium strength concrete.

I suspect the differences in suggested values are due to different end points for the tests and curve match. Concrete strained to the point of being near gravel, is a different animal than concrete with cracking not far from typical serviciability limits. With recent consideration of provention of progressive collapse, or analysis of extreme event capacity (crash resistance, or behavior in extreme earthquakes, or with tornadoes) allowed deformations are much greater than the typical endpoint for designs of the past.

disla

Hi,

I ‘m working to get that concrete beam reference file for MECWAY/CCX.
Segio suggestion is too intimidating for me to start with concrete, so I’m starting with a simpler example.
It is based on an EC2 calculation of a simply_supported T cross section reinforced beam.
The file could be very helpful cause if validated, could be used for testing other concrete material models without questioning (too much) the validity of the analytical result , BC’s , mesh density and suitability of the elements.

Preliminary results are very promising. The deflection’s deviation is below 0.3% (I know that’s the easy part) but I’m struggling to validate the load capacity basically because I don’t know what to look for.Not Civil Enginieer sorry.

Things I would appreciate if someone could bring me some help:

-¿What characterizes the Mcr point?
I understand it is when the concrete cracks initiate but there are so much definitions of tensile that I don’t know which one should I look for.

C25/30 (Y=1.5)




To make even more complicated I can only recognize that Mcr is computed with a 0.9 fctm on the report which don't agree with any of the previous definitions.

Another question that arises to me is that, in mechanical analysis Yield and Ultimate Strengths are Engineering values. Is that the case in Civil engineering. I guess I should convert those values to True Stress to compare ¿isn't it?

Any help is appreciated.

I’m sharing the file and expected solution as reference.
Thanks

https://we.tl/t-PEjx1aTupA

MikeMcMullen

Tensile strength in concrete has many definitions for concrete and in reality they vary a lot depending upon what they are used for, how they are tested, the sample size, prior strain history, and due to extreme variability compared to modern steel, the degree of confidence required that the tensile strength will be met. My favorite is the split cylinder strength as it has somewhat less variability. Its mean is about 0.3(fc)^0.667, but for 20 Mpa cylinder compressive strength concrete it might vary between 1.2 Mpa and 3 Mpa with mean about 2.3Mpa, and for 40 Mpa concrete between 2.6 Mpa and 4.5 Mpa with mean about 4 Mpa. From A. M. Neville's "Properties of Concrete, Fourth edition" pg. 310. These days concrete is typically reinforced with higher tensile strength and stiffness materials to compensate for its high variability in tension. Up to the 1970's unreinforced concrete was covered by codes so long as the tensile stresses were low enough. It still can be in certain specific circumstances, like temporary stresses in the side of prestress members not tensioned, or secondary stresses.

disla

Hi Mike,

I have read that your formula refers to what EC2 calls fctm and it’s a mean value for tensile strength.

fctm [MPa] = 0.30⋅fck^2/3 and it is valid for a range of concrete class ≤ C50/60
fctm [MPa] = 2.12⋅ln[1+(fcm / 10 MPa)] for concrete class > C50/60

That confirms I’m using the right input in my file. Thanks.

I have solved my problem and deviation is below 4%.
The analysis must be performed in two steps if I want to compare with the calculation report.
Theoretically I should obtain the same Mcr value no matter which side of E I’m using but in fact this is not happening.
The problem is that the cutting tensile Stress fctm in this material model is not a clean cut but a soft approach.
Now I understand your previous post better and why you increase artificially fctm to get a more accurate field of points exceeding the allowable tensile.

Mecway /ccx result: Max S11(Mcr) =2.25 MPa. Nodal value. Deviation (2.25-2.34)/2.34 =3.8%

Mecway /ccx result: Max S11(Mcr) =?¿? MPa. Value at the Integration Point. I can’t extract it ?¿?

MikeMcMullen

For this example, of flexure in a solid beam, the tensile strength used normally would be "modulus of rupture". In reality it is dependent on the depth or volume of the tensile zone and is higher than the splitting stress as the extreme stress zone is supported nearby by zones not so highly stressed. It is usually taken as 0.62f'c^0.5. For unreinforced samples it varies quite broadly, sometimes much higher with a large coefficient of variation. As a result in some cases where consequences of tensile cracks are low due to the presence of reinforcing in prestressed members values up to 63% higher are used. For full scale lab testing of reinforced beams when adjusted for depth, or for prestressed concrete beams, it is surprisingly consistent, probably due to the stresss concentrations induced by the reinforcement (tensile strength is probably a function of maximum crack size.)

MikeMcMullen

Note that I actually do not use FEM for dealing with "allowable" stresses in concrete as these have been set by codes based on much simpler calculation methods before FEM was well developed, and may be narrowly applicable. I use it for problems outside the range of the problems considered by the code writers, or where actual behavior is not well predicted by code methods, in order to gain insight into likely actual behavior. In particular I am interested in Mohr-Coulomb is likily to predict shear behavior of concrete better post cracking when run non-linear for both geometry and material. Shear behavior of concrete is often much more important to failures than flexure.

disla

First, I'm mapping all those material properties involved in a report into ccx material properties.

Compression_only material has two constants, apart from density,....

*USER MATERIAL,CONSTANTS=2

**• E. - ----Ec28 According to EC2 Below Mcr
**• E. - ---- Eeff According to EC2 Above Mcr

**• absolute value of the maximum allowed tension

fctm [MPa] = 0.30⋅fck2/3 for concrete class ≤ C50/60
fctm [MPa] = 2.12⋅ln[1+(fcm / 10 MPa)] for concrete class > C50/60

That's a lot.

Concrete problems that can be described in terms of those constants can be approached with ccx.

I have also been looking Mohr Coulomb.
First, I need to find a code calculation to map constants and identify them. I cannot translate my reinforced tee file to Mohr Coulomb until I know what my material parameters are and if I could derive them from E and fctm.

I have start with a paper that I'm liking very much. Simple and full of hints. It has a final validation test. Attached.

MikeMcMullen

The paper is quite helpful. The recommend values are also reasonably consistent with recommended values I have seen. Good luck on the example problem!

disla

Hi,

I have some progress.
I can now predict the failure point (in a Brazilian test for example) and it agrees well once the results are represented into the Mohr Coulomb Diagram. (Failure=Circle touch the line).The problem is that the expected failure is not directly related to a maximum or minimum value of Tensile / Compressive values but a combination of both.

There are many Stress States that may trigger the failure, as much as tangent circles below the line.
My picture shows two stress states obtained from the same model with same Mohr parameters.



That makes difficult to stablish a clean maximum tensile Strength as there is always room between s1 and the point where the Yield Surface touches the abcise.
Not too much but….
The best fit I have found up to now is this.

Given :

Fctm=S1
Fcm=S3
Friction angle according to the literature (Common values are between 30º and 40º).

Solve this to find c:



Example:

Concrete C25/30
Fctm 2.65 [Mpa]
Fcm -33.00 [Mpa]
Friction Angle: 36.00 º
c=10.044960 [Mpa]

*MOHR COULOMB
36.0,0.0
*MOHR COULOMB HARDENING
10.05E6,0.0

Any hint to improve this is appreciated.

MikeMcMullen

I think you are correct...There is no single tensile stress at failure unless you are dealing with a one dimensional problem. I have no insight for improvement.

FERNANDO

It seems like a reasonable fit, but it is a perfect elastoplastic model. When concrete cracks, it stops supporting traction and transmits it to the steel. It would be necessary to have a specific model for concrete.

FERNANDO

In general, for ELS (Service Limit States), average values ​​of materials and service actions are adopted. For ELU (Ultimate Limit State), 5% percentiles are adopted in material parameters, reduced by a coefficient of 1.5 and the actions are increased by the corresponding safety coefficients. Ultimately, it is the method of partial coefficients, an approximation to the statistical reality of the problem.

FERNANDO

In ELS, deformations, cracking, and in ELU, collapse are analyzed.

MikeMcMullen

Actually when concrete cracks in shear the shear stress field rotates putting the crack in some compression. This is what makes Mohr Columb useful, and also what has made concrete analysis in shear difficult after cracking. Currently, for bridges in the US and Canada, shear strength is analyzed by the MCFT or modified compression field theory, which uses this effect plus friction from reaction from the tension provided by stirrups and other steel crossing the cracks to resist the shear. The "modified" reflects that the basic principal has been calibrated by extensive testing. I.e. the cracking, from direct tension, flexure, or shear stress, just changes the behavior. The behavior depends on the crack width, which depends on the unpinned crack length and these compressive stresses. This is why Mohr Coulomb is useful in that it can reflect this friction after cracking. Crack width is sort of an analog for dilation.

This can be analogus to the progressive failure of beams in flexure under transverse load.
The resistance is initially by a. Arching action, then flowing into b. a couple between the elements in tension and those in compression, c. then after flexural cracking a couple between the compression in concrete and the steel, then with larger d. deflection cable or catenary action. Most design only uses c. for strength. All but b. and c. require nonlinear geometry in the analysis. The resistance mechanisms in b. and c. can be analyzed without considering the deformation and fit with a number of untrue but safe assumptions such as all strains are plane, deflection has a small effect, etc. Extreme events with large deformations such as collisions, earthquake, progressive collapse, or explosions need to follow all these mechanisms for practical analysis or design. Sometimes after looking in detail at these mechanisms code writers provide empirical rules so designers can avoid the non-linear analysis, but these empirical rules are not general and involve a lot of assumptions about what is being considered and the desired end point.

disla

I see . There are many details to consider.

Thanks both,

@FERNANDO

When concrete cracks, it stops supporting traction.

Yep. I have noticed on the calculation report. There is a completely different Young modulus before and after Mcr.

@MikeMcMullen
I think there is some room for improvement.

I have read how compressive and tensile tests are done. Compressive is a pure compression test so it is reasonable to consider a uniaxial Stress State . That would be a first Mohr circle with base points s1=0 and s3=-fcm at failure.
For the Tensile test, it is slightly different. The tensile strength is evaluated indirectly from a cylinder under compression in which s3=-3*s1 at the breaking point.
I think it is reasonable to consider a second Mohr circle with base points s1=fctm and s3=-3fctm and not s1=fctm and s3=0. As I was doing.
C and Friction angle can now be obtained finding the direct common tangent to the two circles. No need to search alpha on the literature.




It delivers different Friction angle and Cohesion but, if one input those values on a Brazilian test or a compressive test, one obtains the same breaking points fctm and fcm as it is reported for the material properties.