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1 change: 1 addition & 0 deletions source/user/manual/material/ndMaterial.rst
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Expand Up @@ -46,6 +46,7 @@ The following contain information about matType? and the args required for each
ndMaterials/ASDPlasticMaterial3D
ndMaterials/OrthotropicRAConcrete
ndMaterials/SmearedSteelDoubleLayer
ndMaterials/FAM_CS
ndMaterials/NDTest

Concrete Damage Model
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107 changes: 107 additions & 0 deletions source/user/manual/material/ndMaterials/FAM_CS.rst
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.. _FAM_CS:

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.

.. figure:: FAM_CS_panel_mechanisms.png
:align: center
:width: 85%
:figclass: align-center

Panel-level mechanisms represented by FAM_CS.

.. admonition:: Command

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

.. csv-table::
:header: "Parameter", "Type", "Description"
:widths: 12, 10, 45

$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.

.. csv-table::
:header: "Recorder", "Description"
:widths: 24, 45

panel_strain, "panel strains :math:`\epsilon_x`, :math:`\epsilon_y`, and :math:`\gamma_{xy}`"
panel_stress, "panel stresses :math:`\sigma_x`, :math:`\sigma_y`, and :math:`\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"

.. admonition:: 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.

.. figure:: FAM_CS_validation_six_walls.png
:align: center
:width: 95%
:figclass: align-center

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]_.

.. figure:: FAM_CS_validation_compression_walls.png
:align: center
:width: 80%
:figclass: align-center

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

.. admonition:: Examples

Download the SW1 Tcl example: :download:`FAM_CS_SW1Example.zip <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.

.. code-block:: tcl

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] 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.
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