22.5.1 Contact Density Model

The Contact Density model defines a nonlinear relation between the normalized shear strain $\omega$ and

Figure 22.4: Contact Density shear transfer model

the crack shear stress $\tau$ for every crack shear direction [Fig.22.4]. The relation has various parameters and is different for loading and unloading/reloading, depending on the value of $\omega$ :

$$\centering \boxed{ \rule[-11.4ex]{0mm}{24.0ex} \: \tau = \begin... ...omega_{\mathrm{max}}$ \hspace{8.0ex}(un-/reload.)} \end{cases}\:}$$

The normalized shear strain $\omega$ depends on the crack shear strain $\gamma_{{\mathrm{cr}}}^{}$ and the crack opening $\varepsilon_{{\mathrm{t}}}^{}$ according to:

$$\omega {\frac{{ \gamma_{\mathrm{cr}} }}{{ \varepsilon _{\mathrm{t}} }}}$$ (22.17)

Parameter f_st is related to the compressive strength f_c according to:

$$\begin{cases} 3.8 \, \sqrt[3]{ f_{\mathrm{c}}\rule[-0.7ex]{0... ...t{if $f_{\mathrm{c}}$\ in $\mathrm{kgf / cm^{2}}$}. \end{cases}$$ (22.18)

Parameter $\tau_{{\mathrm{max}}}^{}$ is related to f_st according to:

$$\centering \tau_{\mathrm{max}} = f_{\mathrm{st}} \, \dfrac{ \omega_{\mathrm{max}}^{2} }{ 1 + \omega_{\mathrm{max}}^{2} }$$