3.1.6.22. FAM_CS Material

Code Developed by: Shaohui Zhang, Xiaodong Ji, and Yue Yu at Tsinghua University.

The FAM_CS material is a two-dimensional plane-stress nDMaterial for reinforced concrete panels and walls. FAM_CS stands for Fixed Angle Model Considering Crack Sliding. The material is intended for nonlinear simulation of reinforced concrete shear walls under tension/compression-flexure-shear and flexure-shear loading [Zhang2024FAMCS].

The model keeps crack directions fixed after cracking and represents the reinforced concrete panel response using horizontal and vertical rebar materials together with concrete struts. Nonlinear shear aggregate interlock along concrete cracks [Maekawa2003FAMCS] and rebar dowel action are included to represent shear transfer mechanisms along crack surfaces. When two crack systems are active, the model activates the crack with lower shear stiffness for the aggregate interlock and dowel action calculation.

The panel-level mechanisms represented by FAM_CS are illustrated below. The material response combines the in-plane panel stress and strain field, uniaxial rebar response, dowel action after cracking, and concrete behavior before and after crack formation.

Fig. 3.1.6.6 Panel-level mechanisms represented by FAM_CS.

Command

nDMaterial FAM_CS $matTag $rho $sX $sY $conc $rouX $rouY $dY $Gamax $lm0 $sh

Parameter	Type	Description
$matTag	integer	unique nDMaterial tag
$rho	float	material density
$sX	integer	tag of the uniaxialMaterial for horizontal x-direction reinforcement
$sY	integer	tag of the uniaxialMaterial for vertical y-direction reinforcement
$conc	integer	tag of the ConcreteCM uniaxialMaterial for concrete
$rouX	float	reinforcement ratio in the horizontal x direction
$rouY	float	reinforcement ratio in the vertical y direction
$dY	float	diameter of vertical reinforcement
$Gamax	float	maximum size of coarse aggregate
$lm0	float	calculated average crack spacing
$sh	float	spacing of horizontal reinforcement

Note

The concrete uniaxial material used for $conc must be ConcreteCM. The FAM_CS implementation uses response quantities supplied by ConcreteCM; other concrete uniaxial materials do not provide the required internal responses.

The following recorders are available with the FAM_CS material.

Recorder	Description
panel_strain	panel strains \(\epsilon_x\), \(\epsilon_y\), and \(\gamma_{xy}\)
panel_stress	panel stresses \(\sigma_x\), \(\sigma_y\), and \(\tau_{xy}\)
panel_stress_concrete	concrete contribution to panel stresses
panel_stress_steel	reinforcement contribution to panel stresses
strain_stress_steelX	strain and stress of horizontal x-direction reinforcement
strain_stress_steelY	strain and stress of vertical y-direction reinforcement
strain_stress_concrete1	strain and stress of concrete strut 1
strain_stress_concrete2	strain and stress of concrete strut 2
strain_stress_interlock1	strain and stress from crack sliding mechanism 1
strain_stress_interlock2	strain and stress from crack sliding mechanism 2
cracking_angles	cracking angles for the crack systems

Verification

The FAM_CS model was first validated using six reinforced concrete wall tests under coupled axial tension and cyclic lateral loads [Ji2018FAMCS] [Zhang2024FAMCS]. The comparisons below show the experimentally measured and simulated load-deformation responses for tensile wall specimens modeled with nDMaterial FAM_CS and quad elements.

Fig. 3.1.6.7 Validation for tensile wall specimens under coupled axial tension and cyclic lateral loads.

Additional validation examples include 75 reinforced concrete wall tests under compression-flexure-shear and flexure-shear loading conditions. The following comparisons show validation against high-axial-compression T-shaped wall specimens [Ji2024FAMCS].

Fig. 3.1.6.8 Validation for high-axial-compression T-shaped wall specimens.

Examples

Download the SW1 Tcl example: FAM_CS_SW1Example.zip. The archive contains the Tcl input files and experimental hysteretic curve data; recorder output files are generated when the model is run.

The following commands define one concrete material, two reinforcing steel materials, and one FAM_CS material.

uniaxialMaterial ConcreteCM  2  -54.579  -0.005027  21714.2439  12  1.0134  2.1434  8e-05  1.2  10000
uniaxialMaterial SteelMPF  101  349  349  206000  0.005  0.005  20  0.925  0.15
uniaxialMaterial SteelMPF  103  397  397  206000  0.01  0.01  20  0.925  0.15

nDMaterial FAM_CS  201  0  103  101  2  0.0093084  0.056316  22  16  74.0814  100

recorder Element -file c_strain.out -time -eleRange 1 10 material 1 panel_strain

References

[Zhang2024FAMCS] (1,2)

Zhang, S., Ji, X., Sun, L., Yu, Y., and Cheng, X. (2024). “New OpenSees material model for simulating reinforced concrete shear walls subjected to coupled axial tension and cyclic lateral loads.” Engineering Structures, 318, 118774. https://doi.org/10.1016/j.engstruct.2024.118774.

[Ji2018FAMCS]

Ji, X., Cheng, X., and Xu, M. (2018). “Coupled axial tension-shear behavior of reinforced concrete walls.” Engineering Structures, 167, 132-142. https://doi.org/10.1016/j.engstruct.2018.04.015.

[Ji2024FAMCS]

Ji, X., Sun, L., Wang, S., and Kolozvari, K. (2024). “Seismic behavior and modeling of T-shaped reinforced concrete walls under high axial force ratios.” Earthquake Engineering & Structural Dynamics, 53(3), 1085-1106. https://doi.org/10.1002/eqe.4060.

[Maekawa2003FAMCS]

Maekawa, K., Pimanmas, A., and Okamura, H. (2003). Non-linear mechanics of reinforced concrete. Spon Press.