Indentation of thin copper film using peridynamics

The rapid development of the technology of today increasingly involves the design and fabrication of devices of smaller and smaller dimensions, down to the atomic length scales. At the nanoscale molecular dynamic (MD) models are often used. For many but the smallest systems, MD models are computationally too expensive, whereas classical continuum mechanics models not accurately can resolve microscale phenomena. One modelling strategy is to continualize the MD models, thus replacing inhomogeneities present on smaller length scales by an enhanced continuum description on larger length scales. This approach is called peridynamics (PD). Peridynamics is a novel non-local continuum model; developed by [1], who introduced the term “peridynamic” from the Greek roots for near and force. Peridynamics is a generalized continuum theory employing a nonlocal model of force interaction based on integral operators that sums internal forces separated by a finite distance, which replaces the stress-strain relation in the classical theory of continuum mechanics.
Nano/micro indentation is useful experimental method to characterize the micromechanical properties of materials and have been used to determine elastic and plastic properties, such Young’s modulus and hardness of the material from force-displacement curves. In this study PD is used to simulate nano/micro indentation using LAMMPS [2], with a spherical indenter targeting a copper film. The objective is to show how this approach can be used at different scales. At the nanoscale, the copper coating is modeled with MD as a thin rectangular plate, with the bottom particle layers locked and periodic boundary conditions are applied. The same is done at the microscale but using FE analysis. Elastic and plastic behaviors are investigated and compared to results from both MD and FE analysis. The material parameters in the peridynamic model are chosen to fit represent the results at the two scales.