Non-local modeling of epoxy using an atomistically-informed kernel

An integral type non-local continuum model for epoxy, used as the matrix material in aerospace structural composites, is developed from phonon dispersion data. Non-local continuum models can be used to regularize the stress fields at crack tips and molecular defect cores (e.g. disclinations in epoxies) where local (classical) elasticity theories fail to give bounded solutions. Integral type non-local elastic models phenomenologically incorporate microstructure information through a weighting function known as a kernel function. The kernel functions are typically obtained by matching dispersion curves computed using lattice dynamics. However, the use of lattice dynamics for amorphous polymers that do not have an underlying lattice structure is computationally prohibitive. In this paper, a molecular dynamics based approach is used for the computation of the non-local kernel, for amorphous epoxy. Dispersion relations calculated from the reciprocal-space velocity–velocity autocorrelation function are used to build the kernels. The computed atomistic kernel is used to predict stress solutions for some example problems where classical elasticity predicts singularities.