Concrete07 – Chang & Mander’s 1994 Concrete Model
Concrete07 is an implementation of Chang & Mander's 1994 concrete model with simplified unloading and reloading curves. Additionally the tension envelope shift with respect to the origin proposed by Chang and Mander has been removed. The model requires eight input parameters to define the monotonic envelope of confined and unconfined concrete in the following form:
| uniaxialMaterial Concrete07 $matTag $fc $ec $Ec $ft $et $xp $xn $r |
| $matTag | integer tag identifying material |
| $fc | concrete compressive strength (compression is negative)* |
| $ec | concrete strain at maximum compressive strength* |
| $Ec | Initial Elastic modulus of the concrete |
| $ft | tensile strength of concrete (tension is positive) |
| $et | tensile strain at max tensile strength of concrete |
| $xp | Non-dimensional term that defines the strain at which the straight line descent begins in tension |
| $xn | Non-dimensional term that defines the strain at which the straight line descent begins in compression |
| $r | Parameter that controls the nonlinear descending branch |
NOTES:
- Compressive concrete parameters should be input as negative values.
Unconfined Concrete
For unconfined concrete, the peak compressive strength fc in the above figure is f'c0 and corresponding strain ec is e'c0. Assuming that the compressive strength for unconfined concrete is readily available, the key parameters required for the model can be found using the following recommendations which include:
Confined Concrete
Confinement increases the strength and ductility of concrete. These effects are accounted in the above figure by replaceing the peak compressive strength and the corresponding strain with f' cc and e'cc, respectively. The value of r is also decreased. The recommended approach to define all critical parameters needed to model the confined concrete under compression are as follows:
where:
File:Confined Concrete Parameters.png
The monotonic envelope for the tension side of the confined concrete follows the same curve that is used for unconfined concrete.
Cyclic Behaviour
The hysteretic rules for cyclic behavior of confined and unconfined concrete is built into the model and requires no further input from the user. These rules generally follow the recommendations of Chang and Mander, which was established based on statistical regression analysis on the experimental data from cyclic compression tests of a number of researchers. However, three simplifications were made to the rules proposed by Chang and Mander which are:
- Instead of the power function for unloading and reloading paths, Concrete07 uses tri-linear paths for unloading and reloading. The reason for this change is to increase the computational efficiency of the model, as well as numerical stability.
- The original model shifts the tension envelope as compression reloading after a reversal occurs. This shift is deemed unnecessary and not implemented in Concrete07.
- The original model requires an additional strain be applied beyond the unloading strain to rejoin the monotonic envelope. The Concrete07 rejoins the envelope at the unloading strain; this simplification increases the numerical stability and computational efficiency.
A full description of the Concrete07 material model, modifications to the Chang and Mander concrete model, and the effects of Concrete07 in improving the simulation capacity of OpenSees is given in Waugh (2007).
A comparison of the cyclic behavior of Concrete07 and Concrete03 is shown in below; a magnified view of the tension region is shown separately. A confined concrete is used in this illustration so that the differences between the models behavior is more pronounced.
File:Hysteretic behavior of Concrete07.png
Concrete07 gives larger residual displacements than Concrete03. Concrete07 also has a higher initial stiffness compared with Concrete03 and has a much slower softening post-peak in tension. Chang and Mander state that the abrupt loss of capacity shown in Concrete03 in tension is due to testing conditions and not representative of the true material behavior.
Axial Load
If the material model is used in a section that is going to be subjected to cyclic loading, problems can occur if there is no axial load on the section. The section should be subjected to axial load due to the self weight of the element. If the material is loaded into tension without any compression strain, and then reversed, the model will target -0.00002 strain if cracking has not occurred or 5% of the peak strain if cracking has occurred. The increased value after cracking is due to material being wedged in the open cracks. Users are encouraged to apply some axial load to the section equal to the self weight of the element or a small amount if the user does want minimal axial load. Less than 0.05% of f'cAg is adequate to ensure a stable response. This will then be used instead of the default behavior described above.
REFERENCES:
- Chang, G.A., and Mander, J.B., (1994) "Seismic Energy Based Fatigue Damage Ananlysis of Bridge
- Columns: Part 1 – Evaluation of Seismic Capacity," NCEER Technical Report No. NCEER-94-0006
State University of New York, Buffalo, N.Y.
- Waugh, PhD Thesis (In progress) 2007.
Code Developed by: Jonathan Waugh, Iowa State University and Sri Sritharan, Iowa State University