## 3 Results
### Characteristics of Shear Band
#### 3.2.2 Local Stress-Strain Relationship  
The local strain in the specimens is not uniform (see Figures 7-9) in the plane strain compression tests, which may lead to the differences in the global and local stress-strain relationships. The global stress-strain relationships are obtained from the results of plane strain compression tests (see Figure 6a). Several typical regions in the specimens are selected to obtain the local stress-strain relationships. The local axial strain calculated via DIC analyses is the mean axial strain of all points in the selected region, and the value of the deviatoric stress is obtained from the average stress of the layer where the region is located. The global and local stress-strain relationships for the T1, T3, and T5 tests are shown in Figure 10.  
For the T1 test, the local stress-strain relationships of two regions outside the shear band (A and C) and one region in the shear band (B) are analyzed (the specific locations are shown in Figure 10a). As shown in Figure 10b, the stress-strain curves of regions A, B, and C are similar to the global stress-strain curve before the peak deviatoric stress. However, the stress-strain curves for different regions after the peak deviatoric stress indicate distinct differences. The strain softening in the stress-strain curve for the regions inside the shear band is more gradual than that of the global stress-strain curve, whereas the deviatoric stress in the stress-strain curve for the regions inside the shear band reduces significantly. When the shear band is fully developed, the local axial strain in regions inside the shear band is significantly greater than that in regions outside the shear band. The global axial strain is approximately 7.6%, and the values of local axial strain in regions A, B, and C is 0.84%, 17.3%, and 0.72%, respectively. For the T3 test, one region outside the shear band (A), one region inside the localized shear band (B), and one region inside the shear band (C) are analyzed (see Figure 10c). As shown in Figure 10d, the local axial strain in the region inside the localized shear band (B) that inclined to the right increases faster than that in the other regions; however, it stops increasing after the peak deviatoric stress. The local axial strain in the shear band inclined to the left increases slowly before the peak deviatoric stress but increases rapidly after the peak deviatoric stress. Finally, a fully developed shear band that inclined to the left is formed. The local stress-strain behavior verifies the experimental phenomenon shown in Figure 8. As shown in Figure 10e, the stress-strain curves of one region outside the shear band (A), two regions inside the localized shear bands (B and C), and one region inside the developed shear band (D) are analyzed for the T5 test. As shown in Figure 10f, the local axial strain in region D increases faster than that in regions B and C after the peak deviatoric stress. When the shear band is fully developed, the values of local axial strain in regions A, B, C, and D is 2.8%, 6.1%, 10.0%, and 22.4%, respectively. Only one shear band is fully developed, even though several shear bands emerge during the test.