Homogenization of Polymer Composite Materials Using Discrete Element Modeling

A multiscale approach to calculating the effective elastic properties of a composite material with a fibrous filler and a polymer matrix is presented. Modeling at various scales is performed using a unified algorithmic scheme, solving Cauchy problems for systems of ordinary differential equations. At the atomic level, molecular dynamics modeling is used to calculate the elastic constant tensor of the polymer material. At the mesoscale, the author’s discrete element method is applied to calculate the effective elastic properties of the composite material. The method was tested on problems with regular fiber placement with symmetry, which have an analytical solution. The capabilities of the proposed approach are demonstrated using defect composite homogenization problems, where symmetry is broken. Fiber cracking and matrix–fiber debonding are considered.