13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- displacements and three relative rotations between sites. This yields four spring types with axial, Kn, shear, Ks, twisting, Kt, and bending, Kb, stiffness [17], which could, in general, be different for principal and octahedral directions. Figure 1. Cellular representation of material (a); and unit cell with bonds (b). 2.3 FE model of elastic continuum with rigid particles For our investigation, we use a finite element model of a cube of an elastic material surrounding a truncated octahedral cell of size 2L. The material has a unit modulus of elasticity and Poisson’s ratio = 0.375. Rigid cubic particles are introduced in the cube, so that one particle, P0, is positioned in the centre of the cell, while others are positioned outside the cell in the principal and octahedral directions as shown in Fig. 2. Three different loading conditions are used: (H) hydrostatic compression; (T) pure twist; and (B) pure bending. These are applied via displacement fields on the cube surfaces; examples for pure twist and pure bending are given in Fig. 3. In all cases we calculate elastic energies, , within the unit cell surrounding the central particle. With no particles present, the cell elastic energy is given by the classical continuum solution, since no features exist to disturb stress symmetry. The displacement magnitudes for the three loading cases are selected so that without particles is the same, 0. Figure 2. Particle additions in the principal (left) and octahedral (right) directions. Figure 3. Displacement maps for the loading cases of pure twist (left) and pure bending (right).
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