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Non-linear viscoelasticity for epoxy-based polymers: theoretical modeling and numerical implementation

Koral, Ateş
The present thesis aims at modeling creep behaviour under hydrostatic and uniaxial loadings of a certain silica filled epoxy compound at various temperatures with numerical implementation of algorithms into finite element method. Time dependent behaviour of polymers has been examined and many approaches have been proposed by researchers. Some of the models are inspired from micro-mechanical structure of polymers. These models generally take relaxation of a single entangled chain in a polymer gel matrix upon loading into account. In this thesis, a finite viscoelasticity model, which takes into account volumetric and isochoric creep/relaxation phenomena, is developed for epoxy-based compounds over glass transition temperature. Deformation gradient is multiplicatively split into elastic and inelastic parts and related with associated stretches of the single chain. In this thesis, the non-linear viscous evolution law proposed by Dal is adopted. As a novel aspect, apart from equilibrium bulk modulus parameter, in order to simulate time dependent volumetric creep behaviour of the epoxy compound, a viscous bulk modulus parameter is included in the proposed free energy function. Hence, volumetric effects in viscoelastic behavior is also taken into consideration without needing to split free energy function into volumetric and isochoric parts. Proposed model properly predicts behaviour of epoxy compound above 110 celsius degree in the rubbery state and also in the transition range. It has been demonstrated that the model prediction is quite satisfactory around and above the glass transition temperature, whereas the constitutive behaviour of the epoxy-moulding compounds at temperatures well below the glass transition temperature can not be captured as expected. The model parameters are identified from the experimental results. The algorithmic implementation of the model is carried out in the Eulerian setting in the sense of Dal and Kaliske and the computational performance is demonstrated through representative boundary value problem.