Directional Bias

An important aspect of the model is the generation of the lattice configuration. In many works regular lattices have been used. However, recently Jirasek and Bazant (1995a), and also Schlangen (1995)

Directional Bias

Figure 14.4.5 Failure patterns for various values of a: (a) 0°, (b) 22.5°, (c) 45° using a regular lattice with random strength, elastic stiffness and microl’racture energy of the links (from Jirasek and Bazant 1995a).

demonstrated that a regular lattice always impresses a strong bias on the direction of fracture propagation.

For the square lattices with diagonals analyzed by Jirasek and Bazant, it is, of course, possible to choose the elastic stiffnesses of the links in the main directions of the square mesh and the diagonal directions, the corresponding strength limits of the links and the corresponding microfraclure energies in such ratios that the lattice is isotropic in terms of elastic properties, strength along straight line cuts, and fracture energies dissipated on such cuts for any orientation of the cut. However, even in that case, the fracture tends to run preferentially among the mesh lines. This has been blatantly demonstrated by simulations of fracture of a circular specimen on which a regular square mesh with diagonals was overlaid; see Fig. 14.4.4. In this particle simulation the fracture was caused by an impact at the bottom of the circle in upward direction. In Fig. 14.4.4a the impact was in the direction of the square mesh lines, in Fig. 14.4.4d in the direction of the diagonals, and in Fig. 14.4.4b and 14.4.4c in two intermediate directions. Note the enormous differences in fracture patterns, which were also manifested by great differences in peak loads and energies dissipated. When all the properties of the links of a regular lattice were randomized, strong directional bias of fracture still remained; see Fig. 14.4.5.

Only when a geometrically random lattice was used in Jirasek and Bazanl’s (1995a) study, the directional bias was eliminated, except for small random differences between meshes. Similar results were found by Schlangen (1995) for a double-edge notched specimen subjected to shear. These results indicate that random (unstructured) lattices must be used to avoid directional bias.