Bond-slip model for reinforced concrete - BondCEB

The complex steel/concrete interaction can be modelled with a bond-slip relation, which describes the bond stress (tangential interface traction), $\tau$, in terms of the relative reinforcement slip (tangential interface jump), $s$. This interface material model is based on the local bond-slip relationship for reinforced concrete under good bond conditions outlined in the the fib Model Code for Concrete Structures 2010 [31]. In general, the model is formulated in terms of the interface traction vector $t$ and the interface jump vector $\delta$. In the model, the interface is assumed to have only elastic stiffness $k_$n in the normal direction. The normal interface traction is then evaluated elastically from the normal interface jump, i.e. $t_$n$= k_$n$\delta_$n. The tangential traction $t_$t$= \tau$ is evaluated from the user-specified function $\tau (s)$, see Figure 12:

$$\tau (s) = \begin{cases} \tau_\text{max} \left( \dfrac{s}{s_1} \r... ...xt{for } s_2 < s \leq s_3, \\ \tau_\text{f} & \text{for } s > s_3. \end{cases}$$ (231)

For an exponent $\alpha$ smaller than 1 (default value 0.4), the initial tangential stiffness of the interface, $k_$s, is undefined and cannot be used in numerical computations. Therefore, this stiffness needs to be specified manually. Should the provided stiffness be smaller than $k_$n$= \dfrac{\tau_\text{max}}{s_1}$, it will be automatically adjusted to this value. Note that only elastic tangent stiffness is supported. Hence, in 2D the tangent stiffness matrix takes the form

$$\dfrac{\partial \mbox{\boldmath$t$}}{\partial \mbox{\boldmath$\de... ...= \left[ \begin{array}{cc} k_\text{n} & 0 \\ 0 & k_\text{s} \end{array} \right]$$ (232)

Model description and the input parameters are summarized in Tab. 50.

Figure: Bond stress ($\tau$) - reinforcement slip ($s$) diagram for BondCEB model.

Table 50: Bond-slip model for reinforced concrete - summary.

Description	Bond-slip model for reinforced concrete
Record Format	bondceb (in) # kn(rn) # ks(rn) # s1(rn) # s2(rn) # s3(rn) # taumax(rn) # [ tauf(rn) #] [ alpha(rn) #]
Parameters	- material number
	- kn interface elastic normal stiffness
	- ks interface elastic tangential (shear) stiffness
	- s1 characteristic slip value
	- s2 characteristic slip value
	- s3 characteristic slip value
	- taumax maximum bond stress
	- tauf residual bond stress at reinforcement pull-out
	- alpha bond-slip curve parameter (exponent)
Supported modes	_2dInterface, _3dInterface