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Polyurethane foam is widely used as a primary filling material in car seats. While it provides good damping and energy absorption, the mechanical properties are complex but play a vital role in vibration attenuation and vehicle ride comfort. This study proposes a comprehensive experimental and analytical method to characterize the visco-hyperelastic properties of seat-grade polyurethane foam. Quasi-static and dynamic compression tests were conducted on foam blocks to obtain load–deflection curves and dynamic stiffness. A visco-hyperelastic material model was developed, where the hyperelastic response was derived via the hereditary integral and difference-stress method, and viscoelastic behavior was captured using a Prony series fitted to dynamic stiffness data. The model was validated using finite element simulations, showing good agreement with experimental results in both static and dynamic conditions. The proposed method enables accurate characterization of the visco-hyperelastic material properties of seat-grade polyurethane foam.

The mechanical characterization of brain tissue has been generally analyzed in the frequency and time domain. It is crucial to understand the mechanics of the brain under realistic, dynamic conditions and convert it to enable mathematical modelling in a time domain. In this study, the compressive viscoelastic properties of brain tissue were investigated under time and frequency domains with the same physical conditions and the theory of viscoelasticity was applied to estimate the prediction of viscoelastic response in the time domain based on frequency-dependent mechanical moduli through Finite Element models. Storage and loss modulus were obtained from white and grey matter, of bovine brains, using dynamic mechanical analysis and time domain material functions were derived based on a Prony series representation. The material models were evaluated using brain testing data from stress relaxation and hysteresis in the time dependent analysis. The Finite Element models were able to represent the trend of viscoelastic characterization of brain tissue under both testing domains. The outcomes of this study contribute to a better understanding of brain tissue mechanical behaviour and demonstrate the feasibility of deriving time-domain viscoelastic parameters from frequency-dependent compressive data for biological tissue, as validated by comparing experimental tests with computational simulations.

Prony series representations have been extensively applied to characterizing the time-domain linear viscoelastic (LVE) material functions for asphalt concrete. However, existing methods that can generate high-quality Prony series parameters (i.e., discrete spectra) mostly involve complicated programming algorithms, which poses a challenge for quick access of Prony series parameters. Also, very limited research has been devoted to establishing methods for simultaneously determining both retardation and relaxation spectra. To resolve these issues, this study presented a practical approach to fast acquiring high-quality Prony series parameters for both relaxation modulus and creep compliance of asphalt concrete by using the complex modulus test data. The approach adopts the analytical representations of the continuous relaxation and retardation spectra from the Havriliak-Negami (HN) and 2S2P1D complex modulus models to directly determine the discrete spectra, and the elastic constants, Ee and Dg, for both LVE modulus and compliance functions are further calculated by fitting the corresponding generalized Maxwell model representations to smoothed data from the storage modulus representations of the HN and 2S2P1D complex modulus models. In this way, all the procedures in the proposed method can be easily implemented in Microsoft Excel. The results showed that the HN and 2S2P1D models yielded slightly different continuous spectral patterns at shorter relaxation times and longer retardation times. However, at the region covered by the test data, the continuous spectra of the two complex modulus models were very close to each other. Thus, the two models can generate comparable Prony series parameters within the time or frequency range covered by the test data. Considering that the quality of the resulting Prony series parameters are closely related to the master curve models used for presmoothing, the HN and 2S2P1D models were compared with the conventional Sigmoidal model. Additionally, the Black diagram was recommended for examining the quality of the complex modulus test data before constructing the master curves.