Nonlinear viscoelastic material modeling using nested linkage mechanisms

Abstract

In this study, basic linear lumped elements such as springs and dashpots are used in nested linkage mechanisms in order to simulate and predict the mechanical behaviour of nonlinear viscoelastic materials. The proposed mechanism model containing two nested linkages can show initial softening followed by hardening response under quasi-static loading, which is commonly displayed by hyperelastic materials. Hence, material nonlinearity is simulated by geometric nonlinearity of the linkage mechanism. The mechanism also displays relaxation, hysteresis, and dynamic stiffness responses of viscoelastic materials with the help of dashpot elements. By tuning the geometric parameters of the mechanism, and the stiffness and damping parameters in the system, desired viscoelastic response can be obtained. Most of the previous experimental studies in the literature considered just two of different possible test scenarios. Comparisons with the experimental results in the literature show that the nested linkage mechanism with linear springs and dashpots can successfully simulate the material response in the tests for different double combinations of quasi-static loading, ramp-and-hold loading, hysteresis, and dynamic stiffness tests. When the experimental studies in the literature are investigated, it is seen that studies investigating three different test scenarios are rare. In this thesis, these four testing scenarios are considered in the same study for model validation for the first time. These four tests are conducted on three rubber samples with different stiffness and damping characteristics. It is shown that the nested linkage mechanism model can accurately mimic the material behaviour in these four different tests with a single set of values for the design parameters. In order to evaluate the prediction capability of the nested linkage mechanism model, optimization is conducted using only two test scenarios and the responses in the other two test scenarios are validated. To further assess the prediction capability of the model, parameter values are obtained for a sample and the responses of a sample from the same material with a different size is estimated for the four test scenarios. Finally, considering the hardening behaviour of the samples, the number of parameters in the model is reduced from 8 to 5 and it is shown that the reduced model also gives quite satisfactory results.