13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Figure 9. Relative rotation vs size ratio under pure bending From the three cases considered in this work, it is clear that a separation between all required stiffness coefficients is not possible. However, there is a good indication that the site-bond model should not contain torsion springs and possibly bending springs in the principal directions. One way to check this is pure twist along the octahedral axis, which theoretically should provide twist and bend rotations of all particles. If this proves to be the case, the elastic energy of the continuum with features should be taken by the deformations of the remaining springs. Additional loading cases are necessary to determine the stiffness coefficients of these springs. If these are determined from curvature-free loading cases alone, a good strategy for the calculation of the coupled-stress constant can be proposed. The site-bond model with constants calibrated from curvature-free loading cases can be subjected to a case introducing curvature energy according to theory, for example pure bending, and any excess of energy between the site-bond model and classical continuum should be attributed to curvature energy. 4. Conclusions We have proposed a methodology for calibrating the spring constants of a special lattice model using a micromechanical model of a material containing features. The comparison of the results with the consistent couple-stress theory suggests that some of the possible moment springs in the lattice could be omitted, reducing the complexity and increasing the correspondence between continuum couple-stress theory and discrete representation. We have demonstrated that in all loading cases considered there is an effect of the distance to size ratio of the features, which must be taken into account when calibrating the constants. This suggests that actual microstructure data needs to be used for calibrating the site-bond model. The loading cases considered were not sufficient for complete determination of the spring constants of the discrete model. Further work is necessary with loading cases that provide different linear combinations of activated springs’ kinematics. 1.E‐07 1.E‐06 1.E‐05 1.E‐04 1.E‐03 1.E‐02 0 5 10 15 Magnitude of relative rotations Cell size / Particle size Principal Octahedral
RkJQdWJsaXNoZXIy MjM0NDE=