Overall viscoelastic response of random fibrous composites with statistically quasi uniform distribution of reinforcements. (Q1867628)

The authors describe two methods accounting for the computation of time-dependent response of a polymeric material reinforced by randomly distributed fibers. In order to apply the first method, the authors assume the existence of a representative cell containing some fibers, and further it is supposed that the material can be obtained as a periodic juxtaposition of such cells. Using a special decomposition of displacement field and strain increment inside the material, and partially based on a description of compliance and relaxation functions in terms of Dirichlet kernels, the authors derive a system of two equations from Hill's principle of virtual work. Then, using a finite element method (FEM), the discretization of these two equations leads to a system of linear equations which give the expression of local fields. In the second approach, the authors assume a random mixture of matrix and fibers through characteristic functions. The Hashin-Shtrickman variational formulation is used in extended versions for the primary and dual versions. The last part of the paper presents numerical computations, using a FEM scheme, for different numbers of fibers in the unit cell. The authors compare the overall and local responses of the material obtained with the two approaches. They also obtain a limit version of the second approach.