Micromechanical modeling of viscoelastic composites with compliant fiber–matrix bonding

The micromechanical method of cells is used to calculate the average time-dependent constitutive properties of the homogenized substitute continuum from the viscoelastic material properties and volume fractions of the individual phases as well as from the interphase behavior of polymeric fiber composites. Two approaches are investigated to establish and solve the micromechanical model equations of the rate-dependent material phases. The first one is based on the Laplace-transformation of the time-dependent material functions and the application of the correspondence principle of linear viscoelasticity to the governing equations of the micromechanical model. In the second approach a numerical time integration scheme is developed to compute the convolution integrals. e study of the influence of compliant fiber–matrix bonds alternative models are proposed: A representative volume element with three constituents accounts for the properties of the flexible interphase between the fibers and the matrix. The three-phase model is then compared to a two-phase model with a time-dependent flexible interface to simulate the compliant fiber–matrix bond. Various examples show the performance of both models and the numerical algorithms presented.