# Concrete models

A resultant beam approach to modeling of reinforced concrete beams and columns may be employed in some cases using `*MAT_139` or `*MAT_191`. For an integrated concrete formulation, see `*MAT_195`.

Material models 5, 14, 16, 25, 72, 96, 84 and, in Version 970 of the code, material 145, can be used to model concrete with solid elements. The developmental version 971 includes a third cap model, `*MAT_159` (`*MAT_CSCM(_CONCRETE)`) which has some built-in parameters for concrete.

Mat 16 (Mode 2) is convenient if you know the unconfined compressive strength of your concrete but don't have other concrete material data necessary to derive constants for other concrete models.

*NOTE regarding Mode II of 'MAT_16'

When using `*MAT_16` in Mode 2 (a0 negative) AND your stress units are other than psi, a0 is correctly defined as follows:

• Case 1: version 970, revision earlier than 5185: `psi * -a0 = your stress unit`
• Case 2: version 970, revision 5185 or later: `your stress unit * -a0 = psi`

In version 971, the switch to Case 2 occurs at rev. 2133. The version 971 User's manual, when published, will reflect Case 2. The equation for sigcut shown in the version 970 User's Manual is incorrect. The correct equation is:

• Case 1: `sigcut = 1.7(fc/(-a0))^(2/3) * (-a0)`
• Case 2: `sigcut = 1.7( (fc)^2/(-a0) )^(1/3)`

Aside: Stick with Case 2. This requires that you download rev. 5185 or later of v. 970 The attached models give identical results though the unit systems are different. There appears to be something amiss with Case 1!? (CVS log shows changes made in revs. 3196, 4254, and 5185. I don't remember but making two of those revisions.)

For Mode IIC (`B1 > 0`), the labels "effective plastic strain" and effective stress in the `d3hsp` file are incorrect. The correct labels should be damage (lambda) and scale factor (eta) as described under Mode IIC in the User's Manual. Both are dimensionless.

For Mode IIB (`B1 = 0`), the correct labels for Cards 4 - 7 would be effective plastic strain and scale factor (eta).

Only for Mode I do Cards 4 - 7 represent pressure and yield (or effective) stress.

Materials 5 and 16 have been used successfully for simulating penetration of concrete. Some example material constants for these two material models (in English units) are provided below. LSTC does not take responsibility for the ´correctness´ of these constants.

``` \$  1st example concrete
*MAT_SOIL_AND_FOAM
1 2.16920-4 7.88000+5 6.00000+6 2.43900+6 6025.0000-0.0519000-300.00000
0.0000000 0.0000000
0.0000000 0.0200000 0.0377000 0.0418000 0.0513000 0.1000000 0.5000000 0.0000000
0.0000000 0.0000000
0.0000000 21000.000 34800.000 45000.000 58000.000 1.25000+5 9.44500+5 0.0000000
0.0000000 0.0000000
```
``` \$  2nd example concrete
*MAT_PSEUDO_TENSOR
\$  Mode II Concrete Model Option with automatic EOS
2,2.247E-04,,0.220
5000, -1
3.000E+07,0.200,6.000E+04,4.031E+06,0.000E+00,0.000E+00

\$ 4 blank lines above are required
```
``` \$  3rd example concrete that requires an equation-of-state (EOS)
*MAT_PSEUDO_TENSOR
3,2.247E-04,,0.220
500.,1.250E+03,0.333,6.667E-05,500.,1.50,1.25,0.770
3.000E+07,0.200,6.000E+04,4.031E+06,0.000E+00,0.000E+00
0.000E+00,8.620E-06,2.150E-05,3.140E-05,3.950E-04,5.170E-04,6.380E-04,7.980E-04
9.670E-04,1.410E-03,1.970E-03,2.590E-03,3.270E-03,4.000E-03,4.790E-03,0.909
0.309,0.543,0.840,0.975,1.00,0.790,0.630,0.469
0.383,0.247,0.173,0.136,0.114,8.600E-02,5.600E-02,0.000E+00
*EOS_TABULATED_COMPACTION
3,0.000E+00,0.000E+00,1.00
0.000000000E+00,-4.000000190E-03,-5.499999970E-03,-1.360000018E-02,-2.019999921E-02
-3.559999913E-02,-4.289999977E-02,-5.189999938E-02,-6.190000102E-02,-7.530000061E-02
0.000000000E+00,7250.00000,9425.00000,14065.0000,18415.0000
26100.0000,31900.0000,34800.0000,44950.0000,58000.0000
0.000000000E+00,0.000000000E+00,0.000000000E+00,0.000000000E+00,0.000000000E+00
0.000000000E+00,0.000000000E+00,0.000000000E+00,0.000000000E+00,0.000000000E+00
2550000.00,2550000.00,2550000.00,2550000.00,3340000.00
4280000.00,5220000.00,6210000.00,7500000.00,7500000.00
```

Regarding fc' and '*MAT_005':

For `*MAT_005`, plot sigy vs pressure using the relationship for yield stress given on p. 20.39 of the 970 User's Manual. On the same plot, add a straight line with a slope of 3 which passes thru the origin. This straight line represents the load path of an unconfined compressive test. Where the straight line and yield curve intersect identifies fc'. fc' alone is not sufficient to provide input for `*MAT_005`. `*MAT_006` might be a better choice if that's all you have.

A complete input deck for a notched beam simulation using material 96 is

Mat 96 is probably NOT a good general purpose concrete model.

Mat 84 can produce a binary database that permits the user to visual cracking of the material using LS-PrePost.

Materials 16, 72, 96, and 84 include the option of considering reinforcement (rebar) in a smeared fashion. Alternately, reinforcement can be modeled in a discrete manner using beam elements. These reinforcing beams may be merged to the solid concrete elements (shared nodes), or may be tied to the concrete elements using 1-D contact (which can account for bond slip), or may be coupled to the concrete elements via `*CONSTRAINED_LAGRANGE_IN_SOLID` (CTYPE=2). The last method removes the burden of having to align the beam nodes to the solid element nodes, however, beware the constraint of the rebar to the concrete may conflict with and disrupt other constraints such as symmetry boundary conditions. Example of rebar coupled to concrete is

Mat_25 and mat_145 are geologic cap models. Mat_145 is superior in the sense that the geologic cap is numerically smooth/continuous. Mat 145 elements are indeed eroded when the damage parameter exceeds 0.99; unity is the maximum value. The damage may be turned off by setting Afit=Cfit=Efit=1.0 AND Bfit=Dfit=Ffit=0.0, as explained in the LS-DYNA User Manual. Alternatively, as mentioned in v970 User Manual, the user may set the new input parameter FAILFG=0 (Card 5) and failed elements will Not be removed Although this is intended for SPH & ALE, it seems to fit the user's need; the elements will remain, but their strength will be zero. I plan to add a feature where the failed strength is Not zero, but that awaits funding. (Len 6/6/03)

Concrete may fail in tension (spalling, cracking) but may also fail in compression. A pressure or stress cutoff built into most concrete material models may be sufficient to account for tensile effects. When the concrete fails in compression, it may be desireable to remove the failed elements from the simulation. In v. 971, two compression-based failure criteria have been added to *mat_add_erosion. These criteria are input in the 3rd and 4th fields of Card 1:

3rd field: PMAX (max pressure) (fails if p > PMAX) 4th field: EPSP3 (fails if min prin strain < EPSP3)

Card 2 of *mat_add_erosion contains primarily tension-based failure criteria.

If an element meets any of the criteria specified with mat_add_erosion, the element will be deleted.

Mat 72 is recoded in v. 971 (rev. 2622 or later). This so-called Release III of the Karagozian and Case (K&C) Concrete Model was implemented into v. 971 by Len Schwer. It has a model parameter generation capability based on the unconfined compressive strength of the concrete. V. 971 documentation of mat_72.

More on `old` mat 72 from Len Schwer

To the best of my knowledge, Material Model 72 `*MAT_CONCRETE_DAMAGE` is an extension of Material Model 16 `*MAT_PSEUDO_TENSOR` due to Malvar, Crawford, Wesevich, and Simons, A Plasticity Concrete Material Model for DYNA3D, Int J of Impact Engineering Vol 19, Nos 9-10, pp 847-873, 1997.

This is a NON-associative model and thus does NOT include shear dilatancy.

Two appropriate associated plasticity models for concrete are Material 25 `*MAT_GEOLOGICAL_CAP`, and my personal favorite, Material 145 `*MAT_SCHWER_MURRAY_CAP`.

(Associative Flow used in metal plasticity. (`Flow stress = yield stress`))

Mattias Unosson's thesis on an improved version of MAT72 is available as

http://ftp.lstc.com/anonymous/outgoing/jday/concrete/improved_mat72.pdf

Dr. Len Schwer offers a short course in Geomaterial Modeling geared toward LS-DYNA users. See the class schedule of your local distributor. Concrete falls under the heading of geomaterials and thus discussion of concrete modeling is included in the course. For more information, go to www.geomaterialmodeling.com