9.3.3 Bond-slip

and shear slip $\Delta$ u_t . See also §21.3 for background theory. The relation between normal traction and normal relative displacement is kept linear, as defined by the first value of DSTIF.

Shear relations for positive and negative values of slip are equal. Specification is done in an absolute sense, i.e., refers to the positive part of the diagram.
Unloading and reloading is modeled using a secant approach. Upon a slip reversal, a straight line back to the origin is followed. Beyond the origin, the bond-slip curve (with opposite sign) is inserted.
Material option BONDSL can only be combined with the line interface elements.
There are three bond-slip models available [Fig.9.11]. The cubic bond-slip model can be used in combination with maturity dependency of the cubic function.

**Figure 9.11:** Bond shear traction slip curves
$\begin{figure}\begin{footnotesize}\setlength{\unitlength}{1cm} \begin{picture... ...enterline{\raise 2.7cm\box\graph} } \end{picture}\end{footnotesize} \end{figure}$

Cubic (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...it{mvz}}$_{r}\,$ \texttt{\textit{cz}}$_{r}\,$ {]} \end{tabbing} \end{figure}$

BONDSL 1

indicates the cubic function by Dörr [§21.3.1],

t_t = $\begin{displaymath}\begin{cases} c \Biggl( 5 \left( \dfrac{\Delta u_{t}}{\Delta... ...text{if $\quad \Delta u_{t} \geq \Delta u_{t}^{0}$} \end{cases}\end{displaymath}$

(9.2)

SLPVAL

specifies the parameters in the cubic function: value c is the constant c , value ut0 is the shear slip $\Delta$ u_t⁰ at which the curve reaches plateau. Recommended values are c = f_t and $\Delta$ u_t⁰ = 0.06 mm .

MATSLP

specifies maturity influence of the parameter c of the cubic function. ca ...cz are the values for parameter c , (z $\leq$ 30 )respectively valid for the corresponding mva ...mvz maturity variables. Equivalent age is the only maturity variable that can be used for this model.

(file.dat)

'MATERI'
    1  DSTIF   1000.  250.
       BONDSL  1
       SLPVAL  3.0  0.06
'GEOMETRY'
    1  CONFIG  BONDSL
       THICK   113.1

Power Law (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...\textit{b}}$_{r}\,$ \texttt{\textit{ut0}}$_{r}\,$ \end{tabbing} \end{figure}$

BONDSL 2

indicates the Power Law by Noakowski, which keeps the initial portion linear to avoid infinite stiffness [§21.3.2].

t_t = $\begin{displaymath}\begin{cases} a \left( \Delta u_{t} \right)^{b} & \text{if $... ... \text{if $0 \leq \Delta u_{t} < \Delta u_{t}^{0}$} \end{cases}\end{displaymath}$

(9.3)

SLPVAL

specifies the parameters in the Power Law: value a is the constant a , value b is the power b and value ut0 is the shear slip $\Delta$ u_t⁰ at which the curve is truncated.

(file.dat)

'MATERI'
    2  DSTIF   1000.  19055.
       BONDSL  2
       SLPVAL  10.  0.18  0.0001
'GEOMETRY'
    1  CONFIG  BONDSL
       THICK   113.1

This example defines Noakowski's Power Law with parameters according to Bruggeling: a = 0.38f_ccm with f_ccm the mean cube compressive strength. Power b = 0.18 .

Multilinear (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...extit{ttn}}$_{r}\,$ \texttt{\textit{utn}}$_{r}\,$ \end{tabbing} \end{figure}$

BONDSL 3: indicates a multilinear bond-slip curve.
SLPVAL: specifies a diagram with two values for each point: tt0 ...ttn ( n $\leq$ 100 )are the shear traction values t_t and ut0 ...utn are the shear slip values $\Delta$ u_t . The first point (tt0,ut0) must be the origin (0,0) and the diagram may also contain descending parts (softening). If the initial shear modulus, specified with DSTIF, does not correspond to the initial slope of the diagram, the modulus is replaced by the initial slope of the diagram during the initialization phase of the nonlinear analysis.

(file.dat)

'MATERI'
    3  DSTIF   1000.  300.
       BONDSL  3
       SLPVAL  0.0 0.0  3.0 0.01  5.0 0.05  6.0 0.13  6.0
'GEOMETRY'
    1  CONFIG  BONDSL
       THICK   113.1

Next: 9.3.4 Friction Up: 9.3 Interface Behavior Previous: 9.3.2 Cracking Contents Index

DIANA-9.3 User's Manual - Material Library
First ed.

Copyright (c) 2008 by TNO DIANA BV.