Different hyperelastic material models (Mooney-Rivlin, Yeoh, Gent, Arruda-Boyce and Ogden) are able to estimate Treloar’s test data series containing uniaxial and biaxial tension and pure shear stress-strain characteristics of rubber. If the rubber behaviour is only determined for the specific load of the product, which, in the case of rubber bumpers, is the compression, the time needed for the laboratory test can be significantly decreased. The stress-strain characteristics of the uniaxial compression test of rubber samples were used to fit hyperelastic material models. Laboratory and numerical tests of a rubber bumper with a given compound and complex geometry were used to determine the accuracy of the material models. Designing rubber products requires special consideration of the numerical discretization process due to the nonlinear behaviours (material nonlinearity, large deformation, connections, etc.). Modelling considerations were presented for the finite element analysis of the rubber bumper. The results showed that if only uniaxial compression test data are available for the curve fitting of the material model, the Yeoh model performs the best in predicting the rubber product material response under compressive load and complex strain state.

A design engineer has to deal with increasingly complex design tasks on a daily basis, for which the available design time is shrinking. Market competitiveness can be improved by using optimization if the design process can be automated. If there is limited information about the behavior of the objective function, global search methods such as simulated annealing (SA) should be used. This algorithm requires the selection of a number of parameters based on the task. A procedure for reducing the time spent on tuning the SA algorithm for computationally expensive, simulation-driven optimization tasks was developed. The applicability of the method was demonstrated by solving a shape optimization problem of a rubber bumper built into air spring structures of lorries. Due to the time-consuming objective function call, a support vector regression (SVR) surrogate model was used to test the performance of the optimization algorithm. To perform the SVR training, samples were taken using the maximin Latin hypercube design. The SA algorithm with an adaptive search space and different cooling schedules was implemented. Subsequently, the SA parameters were fine-tuned using the trained SVR surrogate model. An optimal design was found using the adapted SA algorithm with negligible error from a technical aspect.

In rubber bumper design, the most important mechanical property of the product is the force–displacement curve under compression and its fulfillment requires an iterative design method. Design engineers can handle this task with the modification of the product shape, which can be solved with several optimization methods if the parameterization of the design process is determined. The numerical method is a good way to evaluate the working characteristics of the rubber product; furthermore, automation of the whole process is feasible with the use of Visual Basic for Application. An axisymmetric finite element model of a rubber bumper was built with the use of a calibrated two-term Mooney–Rivlin material model. A two-dimensional shape optimization problem was introduced where the objective function was determined as the difference between the initial and the optimum characteristics. Our goal was to integrate a surrogate model-based parameter selection of local search algorithms for the optimization process. As a metamodeling technique, cubic support vector regression was selected and seemed to be suitable to accurately predict the nonlinear objective function. The novel optimization procedure which applied the support vector regression model in the parameter selection process of the stochastic search algorithm proved to be an efficient method to find the global optimum of the investigated problem.

In rubber products design finite element analysis is a widely used technique. In many cases, the pre-defined operating conditions can be achieved by changing the geometric dimensions of the product which is the well-known iterative design method. Using more than one design parameter the number of possible combinations will increase significantly. The application of Support Vector Machine (SVM) can handle the large number of data in a special way and helps to find the optimal design parameters. In this paper an optimization process of a rubber jounce is presented using nonlinear finite element analysis and SVM.

Non-linear finite element calculations are indispensable when important information of the material response under load of a rubber component is desired. Although the material characterization of a rubber component is a demanding engineering task, the changing contact range between the parts and the incompressibility behaviour of the rubber further increase the complexity of the investigations. In this paper the effects of the choice of the numerical material parameters (e.g. bulk modulus) are examined with regard to numerical stability, mesh density and calculation accuracy. As an example, a rubber spring is chosen where contact problem is also handled.