13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- illustrated based on a RVE made of grains and large joints with a grain volume fraction of 58%, and subjected to triaxial loading. The RVE is assumed to have dimensions of 10 mm along each direction. (a) (b) Figure 5. Norm of flow vector for (top) horizontal pressure gradient and (bottom) vertical pressure gradient in anisotropic medium The grains do not present any preferential orientation as illustrated in Fig. 7. They are assumed purely elastic, whereas a plastic behaviour is assumed in the joints ( X is the 4th order elasticity tensor) X:( − YR) (19) with a Drucker-Prager criterion and an associated flow rule #,. .−Z#−[ \ and YR \] ]^ (20) with # _ 3 . `3a@ where _ and a@ are respectively the first invariant of the stress tensor and the second invariant of the stress deviator. The initial Z and [ can be expressed as a function of the cohesion b and of the friction angle c of the material as [ 6bcosc 3−sinc , Z 6sinc 3−sinc (21) To avoid numerical difficulties often met with perfect plasticity, a linear evolution of the yield limit with the plastic strain is introduced through [ [j [ \ (22)
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