Flexible polyurethane foams used for cushioning in the furniture and automotive industries serve as foundations and exhibit complex nonlinear viscoelastic behavior. To design systems that incorporate these materials, it is important to model their mechanical behavior and then to predict the dynamic response of such systems. The example of a pinned-pinned beam interacting with a nonlinear viscoelastic foundation is the focus of the present study. The foundation can either react in compression as well as tension (bilateral), or react only in compression (unilateral). In the latter case, the contact regions between the beam and the foundation are not known a priori, and thus the coefficients of the modal equations obtained in a Galerkin approximation solution approach, are functions of the solution as well. It is therefore computationally expensive to predict the dynamic and steady-state response of these structures to static and harmonic loads. For polynomial-type nonlinearities, it is possible to speed up the computation time by using a convolution method to evaluate integral terms in the model. Also, if only the steady-state response is of interest, direct-time integration can be replaced by incremental harmonic balance to make the frequency response predictions more efficient. The effect of axial load and the influence of various parameters e.g., loading configuration, excitation amplitude, linear and nonlinear stiffness, on the response of the beam on unilateral and bilateral foundations are studied.

The location of the hip-joint (H-Point) of a seat occupant is an important design specification which directly affects the seat comfort. Most car seats are made of polyurethane foam so the location of the H-Point is dependent on the quasi-static behavior of foam. In this study a multi-body seat-occupant model is developed which incorporates a realistic polyurethane foam model. The seat-occupant model consists of two main components: the seat model and the occupant model. In this study the seat is represented by a series of discrete nonlinear viscoelastic elements. The nonlinear elastic behavior of these elements is expressed by a higher order polynomial while their viscoelastic behavior is described by a global hereditary type model with the parameters which are functions of the compression rate. The nonlinear elastic and viscoelastic model parameters were estimated previously using the data obtained from conducting a series of quasi-static compression tests on a car seat foam sample. The occupant behavior is described by a two-dimensional multi-body model with 5 degrees of freedom. A Lagrangian formulation is used to derive the governing equations for the seat occupant model. These differential equations are solved numerically to obtain the H-Point location. These results are then used to calculate the force distribution at the seat and the occupant interfaces. The effects of different system parameters on the system response and the interfacial pressure distribution are also studied.

Vehicle occupants are sensitive to low frequency vibrations, and these can affect ride-quality and dynamic comfort. Static comfort, a function of the support provided by the seat, is also important. The transmission of vibration to seated occupants and the support provided by the seat can be controlled by appropriately designing the seats. Optimization of seat design requires accurate models of seat-occupant systems can be used to predict both static settling points and the low frequency dynamic behavior of the occupant around those points. A key element in the seat, which is a challenge to model, is the flexible polyurethane foam in the seat cushion. It is a nonlinear, viscoelastic material exhibiting multiple time-scale behavior. In this work, the static and the low-frequency dynamic response of the occupant is examined through a planar multi-body seat-occupant model, which also incorporates a model of flexible polyurethane foam developed from relatively slow cyclic compression tests. This model also incorporates profiles of the seat and the occupant, and includes relatively simple friction models at the various occupant-seat interfaces. The settling point, the natural frequencies, the deflection shapes of the occupant at particular frequencies, and the dynamic force distribution between the seat and the occupant are examined. The effects of seat foam properties on the responses as well as those of including a flexible seat-back frame are also investigated.

Nonlinear viscoelastic behavior is a characteristic of many engineering materials and also biological tissue, yet it is difficult to develop dynamic models of systems that include these materials and are able to predict system behavior over a wide range of excitations. This research is focused on a specific example system in the form of a pinned-pinned beam interacting with polyurethane foam. Two cases are considered: (1) the beam and foam are glued so that they are always in contact and the foam can undergo both stretching and compression, and (2) the beam and foam are not glued so that the contact region changes with beam motion, and the foam only reacts in compression. Static as well as dynamic forces act on the beam and the Galerkin method is used to derive modal amplitude equations for the beam on polyurethane foundation. In the second case, determination of the loss of contact points is integrated into the solution procedure through a constraint relation. The static responses for both cases are examined as a function of the foam nonlinearity and loading conditions, and three and five mode solutions are compared. The steady state response of the system subject to static and harmonic loads is studied by using numerical integration techniques. Numerical challenges and the accuracy of this approach are discussed. Frequency responses are generated for a range of foam nonlinearities and loading conditions.

Polyurethane foam used in automotive seating applications is a highly nonlinear and viscoelastic material. These properties are manifested even in its quasi-static response. In this paper, two different approaches to model and identify these material properties are presented. In both the approaches the viscoelastic property is assumed linear and modeled by a convolution of the input with a relaxation kernel that is a sum of exponentials (hereditary integral approach). The elastic force contribution is however assumed nonlinear and modeled by a polynomial in one approach, and by a model derived from Ogden strain energy function in the other. Uniaxial compression data from experiments is used to identify the parameters of the models. The robustness of the identification procedures and the issues associated with them are also discussed.

A fractional derivative model of dissipative effects is combined with a nonlinear elastic model to model the response of polyurethane foam in quasi-static compression tests. A system identification method is developed based on a separation of the elastic and viscoelastic parts of the response, which is possible because of symmetries in the imposed deformation timehistory. Simulations are used to evaluate the proposed identification method when noise is present in the response. The system identification technique is also applied with some success to experimental data taken from several compression experiments on two types of polyurethane foam blocks.

Seat cushion is in the primary load path between the seat and the occupant, and the potential for injuries to an occupant in an accident highly depends on it. The seat cushion is able to dissipate the kinetic energy due to impact in a controlled manner. Wide varieties of energy absorbing materials are used in aircraft interiors for occupant safety and ergonomic purposes. Flexible polyurethane foams are one among those used in seat cushions. Although comfort and aesthetics play an important role in the seat cushion design, safety is among the top criteria. Studies on seat cushions have demonstrated that the seat cushions generally amplify the lumbar/pelvis transmitted load to the occupant, making the seat cushion design further complicated for crashworthy design. The certification of seat cushion requires that their performance be demonstrated by dynamic full scale sled testing. Due to the high costs involved in dynamic testing, a mathematical hybrid multi-body model is developed in this study to simulate the dynamic responses of a bare iron seat, the seat cushion and the occupant represented by crash test dummy. The model is utilized to predict the lumbar load sustained when subjected to the FAR Part 23 and 25 dynamic test conditions for transport and general aviation category aircraft. The model is also used to determine the relative displacement and velocity of occupant against the seat pan. The results from the dynamic model are validated with full-scale sled tests performed at the National Institute for Aviation Research (NIAR), and hence can be utilized as a design tool for the selection of proper seat cushions.