Doubly periodic array of coated cylindrical inclusions model and applications for nanocomposites

An analytical method is proposed to solve the problem of an infinite elastic matrix containing a doubly periodic array of coated cylindrical inclusions under antiplane shear. The elastic fields in the inclusions, the coatings/interphases and the matrix are derived, which are used to investigate the stresses and the effective stiffness coefficients of the nanofiber composites. Numerical examples demonstrate the size dependence of the stress and the effective stiffness coefficient, and the effects of the interphase thickness and stiffness and array configurations of the inclusions on the effective stiffness coefficient. A finite element analysis is used to benchmark the effective stiffness coefficient predicted by the proposed model, in which excellent agreement is observed. When letting the interphase be thin enough, the proposed coated inclusions model can be used to simulate the zero-thickness interface model, which is validated by the results comparisons of the two models. Instabilities of the stress fields are observed under certain conditions in simulating the zero-thickness interface model.