Finite Element Modeling of Rubber Bushing for Crash Simulation - Experimental Tests and Validation
Abstract: Until recently, the general level of detail in full car crash models has not allowed a physical modeling of rubber bushings with solid elements. This is partly because of the difficulty in modeling the complex characteristic of rubber, but also due to limited understanding of the mechanical properties of rubber materials. The main focus of this Master’s thesis project is to develop a new and improved finite element modeling of rubber bushings for crash simulation, including the model of the bolt joint, which keep the rubber bushing linked to the body structure of the car. The final FE-model has to be able to mimic the real mechanical behavior of the rubber bushing and work effectively in the full-vehicle crash simulation. To achieve this, the program for non-linear dynamic analysis of structures in three dimensions LS-DYNA was used. In order to validate the final FE-model of the rubber bushing system testing activities and comparisons between the full-vehicle crash simulation with the new and improved FE-model of rubber bushing and the traditional one that often is used in the simulations were made. The experimental activities were carried out in the tower test of the Safety Centre of Volvo Car Corporation. In the first part of the thesis, comparisons between the finite element analysis and analytical solution of a simple cylindrical model of rubber exposed to shock loading as well as an estimation of the shear modulus G using the strain energy function of the Yeoh model and an energy balance has been done. The results from the FE-simulation corresponded quite well with the ones from the analytical solution when the Yeoh model is used as the hyperelastic rubber material to model the properties of the rubber. Regarding the FE-model of the rubber bushing system, the rubber part of the bushing was modeled in a rough way. This is because holes, fillets and other design features within the geometry of the rubber bushing rapidly increase the number of elements needed and, as a result, the computational cost of the analysis and the stability of the model are affected. Therefore, the smaller parts of rubber at the surface of the plastic outer sleeve, aluminum inner sleeve and at the corners while meshing the rubber bushing were not taken into account. The rubber bushing and the screw joint were modeled using 8-node solid elements, 4-node and 3-node shell elements and, 2-node beam elements. The 8-node solid elements were used for the rubber, the aluminum inner sleeve and the bolt head, the 4-node and 3-node shell elements were used for the plastic outer sleeve, the washer, the big nut and the cylindrical casing of the bolt, and the 2-node beam elements were used for the thread and the grip of the bolt. The Yeoh model was used to describe the hyperelastic behaviour of the rubber and for the rest of the model, the evaluated material models were mostly characterized by using elastic piecewise linear plasticity with a specific curve stress/strain and a yield strength. The contacts between metal and metal surfaces and between the rubber and the plastic outer sleeve were solved by using the simple global contact and the LS-DYNA option TIED_NODES_TO_SURFACE_OFFSET, respectively. The tightening of the bolt joint was taken into consideration in order to properly describe the friction and contacts between the different parts of the complete rubber bushing system from the beginning of the simulation. The rubber itself turned out to be just a small part of the complete rubber bushing system, so it was not necessary to use a complex material model to predict the physical response of the rubber. A simple and purely hyperelastic rubber material model where no damping exists was used instead. The Yeoh model worked out to be a stable model at high strain rate and therefore was used with theses material parameters: C10 = 0,55, C20 = 0,05, C30 = 0,95. The developed FE-model of rubber bushing system seems to model the nonlinearities in the system as large displacement effects and large deformations, material nonlinearity, and boundary nonlinearities. This is confirmed by the preload in the bolt joint, the contacts, the friction between the different surfaces and the bending and pulling out behaviour of the system working properly at the beginning and during the simulation. In order to validate the final FE-model of the rubber bushing system it was exposed to different loading cases in the FE-simulations and full-scale tests. The FE-simulations were tested under the same conditions as in the experimental tests in order to have a reference for comparisons. The full-scale impacts and computed deformations agreed qualitatively but they differed in magnitude. The deformations of the rubber bushing system, due to the bending moment, axial force and pulling out between sleeves appear to be similar to what happens in reality. The reason for the inaccuracies may be caused by several approximations in the FEmodel and others source of error while carrying out the different experimental test. An US-NCAP analysis was also performed in LS-DYNA in order to be sure that the final FE-model of the rubber bushing system works properly in the full-vehicle crash simulation. The simulation provided satisfactory results in the full-frontal impact of the car showing a significant improvement in the behavior of the rubber bushing system in comparison with the full-vehicle crash simulation of the traditional FE-model of rubber bushing that is often used in the car. Finally, the final FE-model of rubber bushing system can be considered reliable and can be used with a high rate of confidence in the full-vehicle crash simulation, since the computational time can be reduced by up to 4 % approximately and when used in the full vehicle crash simulation, this model is more physical and detailed than the traditional one and can better resemble the mechanical behaviour of the real rubber bushing system.
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