A PERIDYNAMICS FORMULATION BASED HIERARCHICAL MULTISCALE MODELING APPROACH BETWEEN CONTINUUM SCALE AND ATOMISTIC SCALE

A PERIDYNAMICS FORMULATION BASED HIERARCHICAL MULTISCALE MODELING APPROACH BETWEEN CONTINUUM SCALE AND ATOMISTIC SCALE

 R. Rahman and A. Haque

Abstract:

In this paper, a multiscale modeling framework has been
established between peridynamics and atomistic models. Peridynamics (PD)
formulation is based on continuum theory implying nonlocal force based
interactions. Peridynamics (PD) and molecular dynamics (MD) have
similarities since both use nonlocal force based interaction. It means
continuum points in PD and MD atoms are separated by finite distance and
exert force upon each other. In this work PD based continuum model of
epoxy polymer is defined by meshless Lagrangian particles. MD is coupled
with PD based continuum model through a hierarchical multiscale
modeling framework. In this framework, PD particles at coarse scale
interact with fine scale PD particles by transferring pressure,
displacements and velocities among each other. Based on the same
hierarchical coupling method, fine scale PD model is seamlessly
interfaced with molecular model through an intermediate mesoscale region
i.e. coarse-grain atomic model. At the end of this hierarchical
downscaling, the information — such as deformation, energy and other
important parameters — were captured in the atomistic region under the
applied force at micro and macro regions. A two-dimensional plate of
neat epoxy was considered for demonstration of such multiscale
simulation platform. The region of interest in the 2D plate was
interfaced with atomistic model by applying the proposed hierarchical
coupling method. The results show reasonable consistency between PD and
MD simulations.

DOI: 10.1142/S2047684112500297