13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- smaller than the magnitude of the relative rotation between P0 and octahedral particles. The latter contains twist and bend components, suggesting an activation of both the torsion and bending springs in the octahedral direction with stiffness coefficients Kt o and Kb o. The much smaller rotation of the principal particles can be used to approximate the kinematics and assume zero rotation of principal particles. Thus the elastic energy is taken by the linear springs in all directions and the torsion and bending spring in the octahedral direction, allowing for calibration of a linear combination of Kn o, Ks p, Kn o, Ks o, Kt o and Kb o, which should depend on the cell to particle size ratio. As in the case of pure twist it can be speculated that the bending springs in the principal direction can be omitted, i.e. Kb p = 0, but this needs to be supported by considering other displacement fields introducing bend-type rotations of principal particles. It can be further speculated, that the torsion stiffness in the octahedral direction should be zero, i.e. Kt o = 0. This could be deduced from the theoretical requirement that pure twists have no energy potential, but requires further investigation. If these were shown to be true, the bending case would provide a calibration for the linear combination of Kn o, Ks p, Kn o, Ks o, Kb o. Figure 8 . Normalised cell energy vs size ratio under pure bending 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 0 5 10 15 Normalised energy, Ω/Ω0 Cell size / Particle size
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