A multiscale modeling scheme based on peridynamic theory

A multiscale modeling scheme based on peridynamic theory

Rezwanur Rahman

Postdoctoral fellow, Center for simualtion, visualization and real time prediction (SiViRt), University of Texas at San Antonio)

John Foster

Assistant Professor, Department of Mechanical Engineering, University of Texas at San Antonio

Anwarul Haque

Associate Professor, Department of Aerospace Engineering and Mechanics, University of Alabama

ABSTRACT

In this paper a multiscale modeling framework has been established
between peridynamics (PD) and atomistic models. Typically, atomistic
models are governed by molecular dynamics schemes (MD). Both PD and MD
formulations are nonlocal. Atomistic model is coupled with PD based
continuum model through a hierarchical multiscale modeling framework. In
this framework, PD models at higher length scale act as external
environment for the PD models at smaller length scale. Based on the
similar idea, a smaller length scale PD model is seamlessly linked with
the atomistic model. At the end of this hierarchical downscaling, the
information such as displacement field, deformation etc were captured in
the atomistic region. The updated atomistic model is interconnected
with all the PD models in the length scale hierarchy. This multiscale
modeling scheme is named as ``PFHMM: A peridynamics based
framework for hierarchical multiscale modeling''. In this paper the
mathematical formulation of PFHMM is discussed rigorously. Also, a
thorough mathematical analysis is carried out in order to show that the
issue with wave reflection between different models at different length
scales is absent in PFHMM. The proposed multiscale modeling scheme is
illustrated for different cases. It is seen that the displacement field
has a strong correlation with the length scale of material. Such
observation was verified with the experimental observation (i.e.
Example-4 on nanoindentation).

http://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,forthcoming,7954...