N. Abolfathi et aL/ Computational Material Science 43(2008)1193-1206 Fig. 2. Three RUCs at fiber cross angles of 0, 45 and 90- 2 Load Case I Load Case 2 Load Case 3 oad Case 4 Load Case 5 Load case 6 Fig 3. The load cases under which the response analyses are carried Load case 1, 2 and 3: are direct concentrated forces in direction 1 Load case 6: is a twist load produced by two concentrated shear 2 and 3 each being applied at the center-node of faces 1, 3 and 5. forces tangential to the faces in 1-and 3-direction being applied simulate microstresses and at the center-nodes of faces 3, and 5. The magnitudes of the pairs strains associated with a condition of uniform uniaxial normal of loads produce equal and opposite torques around the unit stress 011, 022, and 33 as in a tensile coupon. cell. This load case simulates the microstresses for the condition Load case 4 and 5: are concentrated shear forces in direction 1 on of pure transverse shear, 23, in a lamina the faces 3 and 5 each being applied at one of the center-nodes of faces 3 and 5. These load cases simulates microstresses asso- For load cases 1-5 the application of a single load at the center iated with a condition of uniform(pure)longitudinal shear of the face is required as the periodic boundary conditions enforce stress 12 and t13 in a lamina. the three face pairs to deform and to act as they are under a uni-Load case 1, 2 and 3: are direct concentrated forces in direction 1, 2 and 3 each being applied at the center-node of faces 1, 3 and 5, respectively. These load cases simulate microstresses and strains associated with a condition of uniform uniaxial normal stress r11, r22, and r33 as in a tensile coupon. Load case 4 and 5: are concentrated shear forces in direction 1 on the faces 3 and 5 each being applied at one of the center-nodes of faces 3 and 5. These load cases simulates microstresses asso￾ciated with a condition of uniform (pure) longitudinal shear stress s12 and s13 in a lamina. Load case 6: is a twist load produced by two concentrated shear forces tangential to the faces in 1- and 3-direction being applied at the center-nodes of faces 3, and 5. The magnitudes of the pairs of loads produce equal and opposite torques around the unit cell. This load case simulates the microstresses for the condition of pure transverse shear, s23, in a lamina. For load cases 1–5 the application of a single load at the center of the face is required as the periodic boundary conditions enforce the three face pairs to deform and to act as they are under a uni￾Fig. 2. Three RUCs at fiber cross angles of 0, 45 and 90. 1 3 2 Load Case 1 Load Case 2 Load Case 3 Load Case 4 Load Case 5 Load Case 6 Fig. 3. The load cases under which the response analyses are carried. 1196 N. Abolfathi et al. / Computational Materials Science 43 (2008) 1193–1206