The thesis represents the linear and nonlinear formulations of viscoelastic behaviour. Firstly, in the first four chapters, the basis of continuum mechanics, viscoelasticity theory and finite element method in large deformations which are used in the other parts of the research are briefly described. Polymers and elastomers represent important viscoelastic behaviour. However, the pure viscoelastic behaviour in polymers is in a limited range and then, the material exhibits the viscoelastic-plastic behaviour. In the fifth chapter of the thesis, a phenomenological three-dimensional viscoelastic-plastic constitutive model for polymers is presented. The model is based on the assumption that stress can be decomposed into two parts, namely viscoelastic and elastic-plastic. The proposed rate-dependent nonlinear model is then implemented in a finite element (FE) rogram. The validity of the code is assessed by the data from experiments on a specific polymer. The data from three types of tests, namely uniaxial compression, creep, and relaxation, are used to evaluate the validity of the model. Comparisons show that the proposed constitutive model could satisfactorily represent the time-dependent mechanical behaviour of polymers. The model is then used to study the effect of friction in the compression test and the behaviour of polymers under cyclic loading. The viscoelastic behaviour in elastomers is in a larger range and the plastic behaviour is almost negligible. The sixth chapter of the thesis concerns with the formulation and constitutive equations of finite strain viscoelastic material using multiplicative decomposition in a thermodynamically consistent manner. For modeling the constitutive properties of viscoelastic solids in the context of small deformations, the so-called three-parameter solid is often used. The differential equation governing the model response may be derived in a thermodynamically consistent way considering linear spring-dashpot elements. The main problem in generalizing constitutive models from small to finite deformations is to extend the theory in a thermodynamically consistent way, so that the second law of thermodynamics remains satisfied in every admissible process. Based on the proposed constitutive equations, a finite element procedure is developed and implemented in an FE code. Subsequently, the code is used to predict the response of elastomer bushings. The finite element analysis predicts displacements and rotations at the relaxed state reasonably well. The response to coupled radial and torsional deformations is also simulated.
