# Electrical Resistance Response to Strain in 3D-Printed Conductive Thermoplastic Polyurethane (TPU)
## 3 Results  
### Electric Resistance Response Results  
The Ninjatek Eel FFF sensor shows a predictable and consistent behavior during cyclic strain (Figure 3A). A secondary peak can be observed in the strain response.  
Figure 2: Test rig setup used to measure cyclic strain rate and electrical response.  
Figure 3B shows the raw data output of resistance over strain and how the peak strains plotted in Figure 3C were derived. The behavior during cyclic load is variable for the first number of loading cycles (Figure 3B) but converges towards a close to steady-state behavior (Figure 3C) with a repeatable and predictable response (Figure 3D). The initial loading cycle results in an increased resistance at 0 strain, also resulting in an increased resistance throughout the cycle, which drops off as the number of cycles increases.  
Figure 4 shows the electric resistance response during the initial loading cycle.  
The initial loading cycle deviates significantly from the later response. This behavior is, however, also repeatable and predictable. Figure 4 shows that the initial strain response follows the same curve shape for all tested strain rates up to a strain of 0.5. This is evident when comparing the initial loading cycles up against each other. They follow the same curve with a small peak before increasing. The maximum strain does, however, affect the relapsing when unloaded. All the plots in Figure 4 relapses to different electrical resistance values although they follow a trend where they drop to a minimum. When reaching a strain of 0.5, the strain rate influences the behavior, yielding an increase in the resistance for the specimens with larger strains (Figure 4E).  
The results from the validation test, seen in Figure 5, show that there is little variation between the specimens. For the 10 specimens, the largest standard deviation was 110.9 \(\Omega\) at cycle 1. The standard deviation was 58.0 \(\Omega\) at cycle 100. The overall root mean square error (RMSE) for all 10 specimens was calculated to be 66.9 \(\Omega\). Within the tested 100 cycles, the 10 specimens follow the same curve and show similar behavior. The standard deviation appears to result from the difference in initial electric resistance prior to loading.  
The sensor is additionally subject to creep. As seen in Figure 6A, the resistance drops of as a function of time when constant strain is applied. This is also the case during relaxation. It is, however, clear that the creep phenomenon converges with time (Figure 6B).  
Figure 3: Electric resistance response to strain; (**A**) electric resistance during cyclic load as a function of time; (**B**) parabolic electric resistance during cyclic load as a function of strain; (**C**) electric resistance at max. strain trend over multiple cycles of strain; (**D**) electric resistance over strain at close to steady state. The green arrow between (**B**) and (**C**) indicates how the curve in (**C**) is derived from the points in (**B**). The green arrow between (**C**) and (**D**) indicates the maximum strain at cycle 900.  
Figure 4: Electric resistance response during the initial cyclic loading: (**A**) max. strain = 0.05; (**B**) max. strain = 0.1; (**C**) max. strain = 0.2; (**D**) max. strain = 0.5; (**E**) max. strain = 1; (**F**) relative increase in electrical resistance during initial loading cycle for different strain rates.