/MAT/LAW117

This material is only compatible with solid hexahedron elements (/BRICK) and the TYPE43 property (cohesive solid). This material is not compatible with any failure model. All damage and failure are defined inside of the material directly.

Figure 1. Representative scheme of the mixed mode model

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Units
                  kg                  mm                  ms
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CONNECT MATERIAL
#              RHO_I
              7.8E-6
#                 EN                  ET     Imass      Idel     Irupt
                   5                 1.2         0         1         0
#   Fct_TN    Fct_TT                  TN                  TT            Fscale_x
         0         0                   2                 0.7                   0
#                GIC                GIIC               EXP_B              EXP_BK               Gamma
                   1                1.75                   2                   2                   1
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1. Mode I refers to the normal direction and mode II refers to the shear direction. ${\delta }_I$ is the separation in normal direction equal to ${\delta }_{zz}$ direction. ${\delta }_{II}$ is equal to the separation in tangential direction ${\delta }_{II}=\sqrt{{\delta }_{yz}+{\delta }_{zx}}$ . The mixed mode displacement is referred to by ${\delta }_m$ .
2. The damage initiation displacement in mode I and mode II are respectively, ${\delta }_I^0=\frac{T_N}{EN}$ and ${\delta }_{II}^0=\frac{T_T}{ET}$ and for the mixed mode:(1)
   $${\delta }_m^0={\delta }_I^0\cdot {\delta }_{II}^0\cdot \sqrt{\frac{1+{\beta }^2}{{\left({\delta }_{II}^0\right)}^2+{\left(\beta \cdot {\delta }_I^0\right)}^2}}$$

   With the mode mix $\beta =\frac{{\delta }_{II}}{{\delta }_I}$ .

3. The maximum displacement at failure ${\delta }_m^F$ can be calculated using either a Power law for I_rupt=1:(2)
   $${\delta }_m^F=\frac{2\left(1+{\beta }^2\right)}{{\delta }^0}\cdot {\left[{\left(\frac{EN}{GIC}\right)}^{EXP\_G}+{\left(\frac{\beta \cdot ET}{GIIC}\right)}^{EXP\_G}\right]}^{-\left(\frac{1}{EXP\_G}\right)}$$
   or, a Benzeggage-Kenane law for I_rupt =2:(3)

   $${\delta }_m^F=\frac{2}{{\delta }^0{\left(\frac{1}{1+{\beta }^2}\cdot E{N}^{\gamma }+\frac{{\beta }^2}{1+{\beta }^2}\cdot E{T}^{\gamma }\right)}^{\frac{1}{\gamma }}}\cdot \left[GIC+\left(GIIC-GIC\right){\left(\frac{{\beta }^2\cdot ET}{EN+{\beta }^2\cdot ET}\right)}^{EXP\_BK}\right]$$
4. GIC and GIIC are the energy release rates between the peak traction and the maximum displacement for mode I and mode II, respectively.

   $GIC=\frac{TN\cdot {\delta }_I^F}{2}$ and $GIIC=\frac{TT\cdot {\delta }_{II}^F}{2}$