The dynamic mechanical properties of filler-reinforced rubber are characterised by a significant dependence on predeformation, dynamic amplitude and frequency if they are loaded with a large static predeformation superimposed by small harmonic vibrations. If the strain amplitudes are below 0.1%, amplitude dependence does not occur. This is satisfied in the current thesis. In view of this, the main objective of this work is focused on the introduction of a three-dimensional constitutive model of finite viscoelasticity formulated in the frequency domain which is able to represent the vibroacoustic behaviour of the material with respect to predeformation and frequency dependence of the storage and the loss modulus in a broad frequency domain up to 100 kHz. In order to derive a mathematical description of material behaviour, the predeformation and frequency dependent dynamic properties of four different carbon-black filled rubber vulcanisates are first examined through quasi-static and dynamic investigations. The quasi-static experiments are mainly focused on the predeformation dependent equilibrium stress response of the material, whereas the dynamic tests are performed via the dynamic mechanical analysis technique to characterise the predeformation and frequency dependence of the dynamic moduli in the frequency domain. Since this work does not account for stress-softening phenomena like the Mullins effect and the amplitude dependent Payne effect, preliminary quasi-static and dynamic tests are carried out to characterise the influence on these phenomena. Based on these experimental facts, a suitable constitutive model is derived to represent the observed vibroacoustic behaviour with respect to the dependence of the storage and the loss modulus on predeformation and frequency. The formulation is based on the general approach by Haupt and Lion (2002) and starts with a decomposition of the deformation gradient into a volumetric and an isochoric part. Thereafter, a second time-relative decomposition is applied to the isochoric part of the deformation gradient and the specific Helmholtz free energy is defined by the additive decomposition into an equilibrium part and a viscous overstress part. In order to account for the predeformation dependence, a deformation dependent relaxation function is introduced. On this basis, the constitutive equations are first derived in the time domain using the dissipation principle. In order to make the constitutive equations applicable for a transformation into the frequency domain, a geometrical linearisation in the neighbourhood of the predeformed state is applied. Finally, the solution for small harmonic oscillations in the neighbourhood of the static predeformation is evaluated and the dynamic modulus tensor of fourth order is derived. In terms of computational efficiency, a second version of the constitutive approach is introduced by the extension of the classical formulation using the concept of fractional derivatives. In order to identify the material parameters of both formulations, the specified identification equations are derived to simulate the experimental data. Thereafter, the material parameters are determined by the minimisation of errors between experimental data and numerically simulated data. The numerical simulations of both constitutive models are compared to each other to reveal the performance of the extended fractional approach. After identification of the parameters, both constitutive approaches are implemented into the finite element code MSC Marc to perform efficient three-dimensional simulations of complex structures. Finally, the constitutive models are validated by the finite element simulation of dynamic tests with rubber-steel compounds up to 10 kHz.    «

The dynamic mechanical properties of filler-reinforced rubber are characterised by a significant dependence on predeformation, dynamic amplitude and frequency if they are loaded with a large static predeformation superimposed by small harmonic vibrations. If the strain amplitudes are below 0.1%, amplitude dependence does not occur. This is satisfied in the current thesis. In view of this, the main objective of this work is focused on the introduction of a three-dimensional constitutive model of...    »