Estimation of Nonlinear Viscoelastic Parameters from Estimated Linear Models of Behavior around Multiple Settling Points of a Foam-Mass System

Flexible polyurethane foam is the main cushioning element used in car seats. Optimization of an occupied seat's static and dynamic behavior requires models of foam that are accurate over a wide range of excitation and pre-compression conditions. In this research, a method is described to estimate the parameters of a global model of the foam behavior from data gathered in a series of impulse tests at different settling points. The estimated model is capable of describing the responses gathered from all the impulse tests using a unique set of parameters. The global model structure includes a nonlinear elastic term and a hereditary viscoelastic term. The model can be used to predict the settling point for each mass used and, by expanding the model about that settling point, local linear models of the response to impulsive excitation can be derived. From this analysis the relationship between the local linear model parameters and the global model parameters is defined. A series of experiments are conducted using different sized masses on the foam block. For each mass, the settling point is measured and the free response after an impulsive excitation is modeled as a Prony series whose parameters can be related to the parameters in the local linear dynamic model. By using the relationship between the local and global model parameters and estimates of the local models' parameters, the parameters of the global model are estimated. The estimation method is first applied to simulation data and then used to identify models of the uniaxial dynamic behavior of polyurethane foam blocks.