a b s t r a c tThe focus of the present paper is the experimental investigation, the constitutive representation and the numerical simulation of the amplitude dependence of filler-reinforced elastomers. A standard way to investigate the dynamic properties of viscoelastic materials is via the dynamic modulus which is obtained from stress signals due to harmonic strain excitations. Based on comprehensive experimental data, an amplitude-dependent constitutive model of finite viscoelasticity is developed. The model is based on a modified Maxwell chain with process-dependent viscosities which depend on additional internal state variables. The evaluation of this thermodynamically consistent model is possible in both the time domain, via stress-time signals, and in the frequency domain, via the dynamic modulus. This property is very profitable for the parameter identification process. The implementation of the constitutive model into the commercial finite element code ANSYS with the user-programmable feature (UPF) USERMAT for large deformations in updated Lagrange formulation is presented. This implementation allows simulating the time-dependent behaviour of rubber components under arbitrary transient loading histories. Due to physical and geometrical nonlinearities, these simulations are not possible in the frequency domain. But, transient FEM computations of large loading histories are sometimes not possible in an acceptable time. In the context of the parameter identification the fundamental ideas are presented, how this problem has been solved. Transient FEM simulations of real rubber components are also shown to visualize the properties of the model in the context of the transient material behaviour.

Filler‐reinforced rubber shows many interesting nonlinear effects under cyclic deformations. As a result of the dynamic loading, a change in the materials' microstructure and hence in the dynamic behaviour of the elastomer is observed. In this context, the frequency‐, amplitude‐, temperature‐, and the preload‐dependence are well‐known effects. Additionally, pronounced thermomechanical couplings are observed, e.g., heat build‐up phenomena. Mechanical coupling effects can be demonstrated by studying the transient dynamic behaviour of the Payne‐effect (amplitude dependence). Using the technique of dynamical mechanical analysis (DMA) the mentioned effects can be investigated in a very comfortable way. To study the process dependence of the dynamic modulus, bimodal DMA tests and transient multistep tests have been carried out. The non‐trivial postprocessing of the bimodal measurements is shortly explained in the paper. The approach of finite nonlinear viscoelasticity with additional internal variables provides an excellent basis for constitutive material modelling. The thermodynamical consistency of the developed constitutive model is demonstrated. This offers the possibility to represent thermomechanical coupling effects like the dissipative heat build‐up. A series of numerical results of FEM simulations under more complicated transient loading histories, computed with the developed and implemented material model, are presented.

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