3.1.7.21. SmearedSteelDoubleLayer Material

This command is used to construct a SmearedSteelDoubleLayer material object. It is the abstract representation of a double perpendicular smeared steel layer (plane stress) 2D material with a tangent formulation. Each layer works only in the direction of the bars, so a uniaxial constitutive model is used to represent the behavior of reinforcing steel bars in each direction. The angle that defines the orientation of the steel layers with respect to the local coordinate system x-y is denoted as \(\theta_{s}\), represented by the argument $OrientationEmbeddedSteel (based on the work of Rojas et al., 2016).

Fig. 3.1.7.7 SmearedSteelDoubleLayer Material: (a) Distributed reinforcement; (b) Rebar layers; (c) Steel layers orientation; (d) Steel behavior in the local coordinate system; (e) Uniaxial steel behavior.

Command

nDMaterial SmearedSteelDoubleLayer $matTag $s1 $s2 $ratioSteelLayer1 $ratioSteelLayer2 $OrientationEmbeddedSteel

Parameter	Type	Description
$matTag	integer	unique tag identifyieng this material
$s1	integer	tag of unixial simulating horizontal reinforcement
$s2	integer	tag of unixial simulating vertical reinforcement
$ratioSteelLayer1	float	reinforcing ratio in horizontal direction of smeared steel
$ratioSteelLayer2	float	reinforcing ratio in vertical direction of smeared steel
$OrientationEmbeddedSteel	float	orientation of the smeared steel layers

The following recorders are available with the SmearedSteelDoubleLayer material.

Recorder	Description
steel_layer_stress	in-plane panel steel stresses \(\sigma^{s}_{xx}\), \(\sigma^{s}_{yy}\), \(\tau^{s}_{xy}\)
strain_stress_steel1	Uniaxial strain and stress of steel 1 \(\varepsilon_{s1}\), \(\sigma_{s1}\)
strain_stress_steel2	Uniaxial strain and stress of steel 2 \(\varepsilon_{s2}\), \(\sigma_{s2}\)

Notes

1. The implementation of this material does not include the reductions in yield strength and strain-hardening ratio for embedded steel bars in concrete (Belarbi and Hsu, 1995).

Examples

The following example constructs a SmearedSteelDoubleLayer material with tag 2 , composed of a horizontal and vertical uniaxial steel material (e.g. Steel02, SteelMPF) of tag 1, reinforcing ratio in horizontal and vertical direction of 1% and an orientation of the double smeared steel layer of 0.0 radians.

1. Tcl Code

nDMaterial SmearedSteelDoubleLayer 2 1 1 0.01 0.01 0.0;

2. Python Code

nDMaterial('SmearedSteelDoubleLayer', 2, 1, 1, 0.01, 0.01, 0.0)

REFERENCES:

1. Rojas, F., Anderson, J. C., Massone, L. M. (2016). A nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the modeling of reinforced concrete walls. Engineering Structures, 124, 521-538. (link).

2. Belarbi, A., & Hsu, T. C. (1995). Constitutive laws of softened concrete in biaxial tension-compression. ACI Structural Journal, 92(5), 562–573. (link)

Code Developed by: F. Rojas (University of Chile), M.J. Núñez (University of Chile).