Coupled viscoelastic-viscoplastic modeling of homogeneous and reinforced thermoplastic polymers

(eng) Glass fiber reinforced thermoplastics are widely used in structural applications because of their high stiffness and failure stress. However, controlling their complex mechanical behavior must rely on numerical simulations. The main outcome of this thesis is an original mean-field approach predicting the mechanical response of fibre reinforced thermoplastics under arbitrary loading paths. The model accounts for the volume fraction and the orientations of fibers as well as the viscoelastic- viscoplastic (VE-VP) character of the surrounding matrix. The matrix response is described in terms of a coupled VE-VP model suitable for multi-axial strains. The total strain is the sum of viscoelastic and viscoplastic parts, and the Cauchy stress is computed by assuming linear viscoelasticity and relying on a Boltzmann integral of the history of viscoelastic strains. An efficient and robust time-integration algorithm is developed, implemented in a numerical code and studied. In order to evaluate the composite's behavior, an affine linearization procedure is proposed for the coupled VE-VP model. This formulation leads to an incremental constitutive relation in the time domain which is form-similar to linear thermo-elasticity. Hence, existing homogenization models for linear thermoelastic composites can be applied. We also conducted direct finite element (FE) analysis of representative volume elements (RVEs) to verify the predictions of the proposed mean field homogenization (MFH) method.