# Measurement of Relaxation Modulus of Viscoelastic Materials and Design of Testing Device
## 2 Related Studies  
In the time domain indentation measurement methods, [PERSON] [22] proposed a variable rate loading method using the spherical indenter. In this method, the most important thing is to ensure that the displacement of the indenter changes according to the requirements of the variable speed rate. This method requires extremely high-speed control accuracy of the indentation instrument. The speed requirement at the initial moment is extremely high, and the rate variation range during the testing process should be wide so that long-term load-displacement data can be measured. Due to the limitations of the indentation device, the maximum speed achievable in the initial stage is very limited. Therefore, in general experiments, the relaxation modulus function of the material will not be obtained over a long time range.  
[PERSON] et al. [23] studied the flat punch loading method and derived a set of methods for measuring material relaxation modulus using the ramp constant loading test method. In the study, the ramp constant loading test was divided and the theoretical calculation formulas for measuring the relaxation modulus of the ramp and constant parts were obtained. [PERSON] et al. derived the theoretical formula for measuring the relaxation modulus using the ramp constant loading method under a flat punch. Since the theoretical formulas for the ramp and constant parts have the same unknown variables, the two formulas can be used to fit the overall measured data and obtain the required variable values when calculating the relaxation modulus. By substituting the generalized Maxwell model of linear viscoelastic materials, the relaxation modulus function of the required solution can be obtained.  
The experimental data obtained using the ramp constant loading test method needs to be measured through a force sensor. Therefore, the force change curve data for the ramp loading section will be affected by the accuracy of the force sensor, thereby affecting the minimum value of the data measured in the time domain. Constant data can be measured for an infinite time under ideal conditions. Therefore, the calculation of the relaxation modulus function based on the obtained experimental data is only affected by the accuracy of the force sensor and is not limited by the measurement method.  
Using the above analysis, the ramp constant loading test method can be used to calculate the relaxation modulus function values in the entire time domain during the experimental measurement process compared with the variable rate loading method. However, the rigid flat punch indenter used by [PERSON] et al. was prone to material damage during the experiment due to its sharp edges. Second, when using a flat punch for testing, it is difficult to ensure that the flat punch moves vertically into the material plane, which seriously affects the accuracy of the measurements.  
Therefore, in order to comprehensively determine the viscoelastic properties of materials, we need a suitable measurement method. Analyzing various relaxation modulus testing methods under the existing instrument indentation method showed that the ramp constant loading test method is more suitable for measuring the relaxation modulus of materials compared with other testing methods. However, due to the shortcomings of the flat punch, we propose the use of a spherical indenter to measure the relaxation modulus through ramp constant loading.