## 3 Results and Discussion  
### Viscoelastic Behavior and Fatigue Failure  
Viscoelastic testing was carried out by subjecting the erythrocyte suspension to a short pulse of electrical excitation at 2 \(V_{rms}\) and dynamic testing was conducted using the cyclic pulses of above electrical excitations. A sinusoidal wave pulse for 4 s (Figure 3a) and a square wave pulse for 10 s (Figure 4a) were utilized for both experiments. The maximum value of the carrier sinusoidal waveform was 2.8 kV/m, which was much lower than the critical field strength--20-40 kV/m is needed for breakdown of the plasma membrane [35; 36]. Deformation of the cell was quantified as the maximum  
Figure 2: Experimental observations of electrodeformation of erythrocyte membranes in interdigitated electrode settings. (**a**) Cells are freely suspended in the medium when the electric field is off. (**b**) Cells are stretched by the DEP force when the electric field is supplied. (**c**) Representative electrodeformation of the cell membrane, \(d\), as quantified by the maximum displacement of the cell membrane to the edge of the electrode. Insets show representative deformation of the cell membranes with time. displacement of cell membrane to the edge of the electrode relative to the initial displacement when the cell started to respond to the electric field, \(d/d_{0}\). Erythrocytes exhibited time-dependent viscoelastic behavior (Figures 3b and 4b). During the 1 st application of electromechanical stress to a sinusoidal waveform excitation, cell membranes deformed gradually, reached their maximum state of \(2.05\pm 0.34\), and recovered gradually upon the unloading process, as determined from 10 different measurements. Upon a gradual release of the loading, erythrocyte membranes recovered gradually and eventually returned to their initial state with no noticeable plastic deformation (Figure 3c). During the 450 th cycle, the maximum deformation of erythrocyte membranes was reduced to 1.74 \(\pm\) 0.46. Cell membranes responded to the loading and unloading much slower than the initial cycles. After the 450 cycles of loading, they could not return  
Figure 4: Electrodeformation of erythrocyte membranes during cyclic square waveforms. (**a**) Electrical excitation was supplied to the erythrocyte suspension, each cycle consists of a duration for 10 s and a relaxation for 10 s. \(V_{rms}\) value is 2 V. (**b**) Displacement of erythrocyte membrane to the electrode edge as a function of time (\(n=5\)) during the 1 st and 180 th cycles, respectively. Error bar represents the standard deviation. (**c**) Morphological of cells before electrodeformation and after the 1 st and 180 th cycles of electrodeformation. Figure 3: Electrodeformation of erythrocyte membranes during cyclic sinusoidal waveforms. (**a**) Electrical excitation was supplied to the erythrocyte suspension, each cycle consists of a duration for 4 s and a relaxation for 4 s. \(V_{rms}\) value is 2 V. (**b**) Displacement of erythrocyte membrane to the electrode edge as a function of time (\(n=10\)) during the 1 st and 450 th cycles, respectively. Error bar represents the standard deviation. (**c**) Morphological of cells before electrodeformation and after the 1 st and 450 th cycles of electrodeformation. to their initial states after long relaxation. Erythrocytes turned into ellipsoidal shapes (Figure 3c, Cells 2-5). During the 1 st cycle of square waveform excitation, cell membranes responded instantly and reached to their maximum deformation level, 1.83 \(\pm\) 0.23, determined by five different measurements (Figure 3). Upon a sudden release of loading, erythrocyte membranes recovered quickly and returned to their initial state with no noticeable plastic deformation. After 180 cycles of excitation, the maximum deformation level was reduced to 1.71 \(\pm\) 0.20, and quick recovery was observed. However, permanent damage was formed in the cell membranes, in the form of thorny projections at the far edge of erythrocyte membranes (Figure 4c, Cells 2 and 5).