21.1 Discrete Cracking

The constitutive law for discrete cracking in DIANA is based on a total deformation theory, which expresses the tractions as a function of the total relative displacements, the crack width $\Delta$u_n and the crack slip  dt [Fig.21.2].

Figure 21.2: Discrete cracking

In DIANA, both the relationships between normal traction and crack width and between shear traction and slip are assumed as a nonlinear function:

$$\begin{cases} t_{n} &= f_{n} ( \Delta u_{n}) \\ [1ex] t_{t} &= f_{t} ( \,\mathrm{d}t) \end{cases}$$ (21.6)

Differentiating (21.6) results in expressions for the tangential stiffness coefficients:

$$\begin{cases} D_{11} &= \dfrac{ \partial f_{n} } { \partial\... ...= \dfrac{ \partial f_{t} } { \partial\,\mathrm{d}t} \end{cases}$$ (21.7)

In general, the normal traction t_n is governed by a tension softening relation. For structural interface elements, DIANA-9.3 supports a brittle relation, a linear softening relation and a nonlinear relation as outlined in the following.