Modeling of Elasticity and Damping for Filled Elastomers

Elasticity and damping are significant properties of rubber, taken advantage of in engineering applications. It is therefore important that the constitutive model accurately captures these aspects of the mechanical behavior. In the first part of the thesis a description of theory and experiments for determination of hyperelastic parameters required for finite element analysis is provided. Test specimens and corresponding stress-strain relations for calibration of the hyperelastic models are discussed. Mechanical conditioning procedures are compared and fitting of the models are discussed, with special emphasis on a ``cubic I1'' model proposed by O.H. Yeoh. A strain energy plot to check the quality of the fitted model is presented, which reveals whether the model is valid for use in finite element analysis. The accuracy of existing test specimens, and a new axisymmetric combined compression and tension specimen proposed here, are investigated by finite element analysis. A modified hardness test for evaluation of hyperelastic constants is presented and evaluated by finite element analysis. Moreover, a method for contact-free strain measurement for evaluation of surface strain fields is presented. Experimental deformation gradients can also be obtained by this method. The second part of the thesis concerns modeling of dynamic material properties of filled rubbers. Experiments show that constitutive models available in commercial finite element codes are not able to model the behavior of filled rubber vulcanizates in dynamic applications. One-dimensional models are used to examine the mechanisms of damping in these rubbers. The ability of the models to capture the frequency and amplitude dependence of the dynamic modulus and equivalent phase angle is investigated. The microstructure and the experimental results support a model with nonlinear elastic, viscous (rate-dependent) and frictional (rate-independent) elements connected in parallel. A generalization of this one-dimensional viscoplastic model to multiaxial and large strains is proposed and evaluated in simple shear and uniaxial stress