The reinforced concrete material model is treated as statistically homogeneous with different tensile and compressive behaviors. It follows a smeared crack model where cracking and crushing are simulated via degeneration of the elasticity at integration points instead of tracking individual macroscopic cracks. (Cracks can occur in up to three different orthogonal planes at each integration point of each element. The number of integration points are set on the Element Definition.) The model described here is intended for relatively monotonic loadings. (A true monotonic load either increases or decreases but does not reverse.) In the current model, cracking is considered the most important aspect, but compression under confinement is also reasonably accounted for. See Figure 1.
The reinforced concrete material model also implements a smeared rebar approach. The rebar is assumed to be distributed (smeared) over entire element with a given volume fraction. The strength of the rebar reinforces the concrete in the specified direction. The rebar material itself follows an elastoplastic material model with von Mises isotropic hardening. Three independent directions of rebars can be defined.
Tip: Alternatives to smeared rebar approach
Although the smeared rebar approach is a common analytical procedure, its approximation may not be acceptable in some situations. One of the following approaches could be used for a more accurate solution:
- Instead of using one part, in which the rebars are distributed throughout the volume of the part, use two parts. Both parts are defined as reinforced concrete. The first part consists of concrete with no rebars. The second part occupies a volume of concrete surrounding the rebars and uses the smeared rebar technique in its volume.
- Model the concrete as one part without rebars, and model the rebars as a second part using beam or truss elements. Ideally, the beam or truss elements should connect to every node of concrete along the length of the rebar; this may require some extra work in creating the mesh depending on the number and complexity of the rebars.
Figure 1: Idealized Uniaxial Behavior of Plain Concrete
The material properties for reinforced concrete are as follows. In the following descriptions, plain concrete refers to the concrete without any rebars. The combined properties of the concrete and rebars are handled by the processor.
General Tab
The input on the General tab are for the plain concrete.
- Mass density Enter the mass per unit volume of the plain concrete (rebar excluded).
- Young's modulus Enter the Young's modulus. This is the slope of the stress versus strain curve of a material in the elastic region (points 2-3-4 in Figure 1). It is also referred to as the modulus of elasticity. This value must be greater than zero.
- Poisson's Ratio Enter the Poisson's Ratio. Poisson's ratio is found by taking the negative lateral strain and dividing it by the axial strain for an axially loaded member.
Strength Tab
The input on the Strength tab are for the plain concrete.
- Uniaxial Tensile Strength Enter the strength (breaking stress) of the concrete subjected to an uniaxial tensile load (point 4 in Figure 1). This value must be greater than zero.
- Uniaxial Compressive Strength Enter the strength (crushing stress) of the concrete subjected to an uniaxial compressive load (point 1 in Figure 1). This value is entered as a positive number and must be greater than zero.
- Biaxial Compressive Strength Enter the strength (crushing stress) of the concrete subjected to equi-biaxial compressive loads. This value is entered as a positive number or zero. If entered as zero, then the input on the Advanced tab will determine the biaxial compressive strength.
- Tension Stiffening This drop-down contains two options pertaining to the formation of cracks and what happens to the strength. When Fracture energy, Linear is chosen, enter the value for the Fracture energy/area of the plain concrete, which is the fracture energy (between the initiation of one crack and complete failure) per unit area. A value of zero is equivalent to setting the Tension Stiffening value to None. The fracture energy per volume is proportional to the area under the stress-strain curve from points 4 to 5 (see Figure 1), and multiplying this by the characteristic length gives the value of Fracture energy/area.
- Shear retention When a crack forms and closes, the material may be able to transmit shear forces parallel to the plane of the crack. A Parameter of 1 indicates a rough crack; it is able to transmit all the shear forces without any loss. A value of 0 indicates a perfectly smooth crack with no friction; no shear forces can be transmitted along the crack plane.
Hardening Tab
The input on the Hardening tab are for the plain concrete. This input describes the stress-strain curve of the concrete in compression after the elastic region (points 2 to 1 in Figure 1).
Enter the Strain and Stress values as negative values, starting at the yield point (point 2). Using the Sort button will sort the values in descending order (yield point to failure point). A minimum of two data points are required.
The entries on the first row (Index 1) is the yield point and are linked to the Young's modulus entered on the General tab. Therefore, the strain for the first row cannot be entered; it will be calculated by the processor as (Stress row 1)/(Young's modulus). The interface will calculate and enter the strain for the first row if you try to select that cell; the processor will calculate the initial strain regardless of the value entered.
Rebar Tab
The input on the Rebar tab are for the rebar materials. A bi-linear stress/strain curve is used in the analysis, where the material follows the modulus of elasticity up to the yield stress and then follows the strain hardening modulus.
- Number of rebars Choose the number of rebars to include in the material using the pull-down. The corresponding number of rebar tabs will be available for inputting the data.
- Volume ratio is the fraction of the total volume occupied by the rebar. This value must be between 0 and 1, and the sum of the volume ratios for all the rebars must be less than 1.
- Mass density Enter the mass per unit volume of the rebar material only.
- Modulus of elasticity Enter the modulus of elasticity of the rebar material in the elastic region.
- Strain hardening modulus The strain hardening modulus is the slope of the stress/strain curve after the yield stress.
- Yield stress Enter the yield stress of the rebar material.
- Rebar direction X, Rebar direction Y, and Rebar direction Z are the X, Y, Z components of a vector that defines the direction of the rebar. So [1,0,0] indicates that the rebars are parallel to the X axis, and [1,1,0] will place the rebars in the XY plane at a 45 degree angle from the X axis. The magnitude of the vector must be greater than 0 but otherwise is not used.
Advanced Tab
The failure envelope for plain concrete can either be calculated from the strengths entered on the Strengths tab, or computed from actual test data. Use the Method pull-down to specify which parameters to use in the calculation. Refer to the page Reinforced Concrete Theoretical Description for information on how to calculate the coefficients based on measured data.