The fully nonlocal, finite-temperature, adaptive 3D quasicontinuum method for bridging across scales

Computational modeling of metallic materials across various length and time scales has been on the rise
since the advent of efficient, fast computing machines. From atomistic methods like molecular statics and
dynamics at the nanoscale to continuum mechanics modeled by finite element methods at the macroscale,
various techniques have been established that describe and predict the mechanics of materials. Many recent
technologies however, fall into a gap between length scales (referred to as mesoscales), with
microstructural features on the order of nanometers (thereby requiring full atomistic resolution) but large
representative volumes on the order of micrometers (beyond the scope of molecular dynamics). There is
an urgent need to predict material behavior using scale-bridging techniques that build up from the atomic
level and reach larger length and time scales. To this end, there is extensive ongoing research in building
hierarchical and concurrent scale-bridging techniques to master the gap between atomistics and the
continuum, but robust, adaptive schemes with finite-temperature modeling at realistic length and
time scales are still missing.

In this thesis, we use the quasicontinuum (QC) method, a concurrent scale-bridging technique that extends
atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set
of representative atoms, and using interpolation to recover the motion of all lattice sites where full
atomistic resolution is not necessary. We develop automatic model adaptivity by adding mesh refinement
and adaptive neighborhood updates to the new fully nonlocal energy-based 3D QC framework, which
allows for automatic resolution to full atomistics around regions of interest such as nanovoids and moving
lattice defects. By comparison to molecular dynamics (MD), we show that these additions allow for a
successful and computationally efficient coarse-graining of atomistic ensembles while maintaining the
same atomistic accuracy.

We further extend the fully nonlocal QC formulation to finite temperature (termed hotQC) using the
principle of maximum entropy in statistical mechanics and averaging the thermal motion of atoms to obtain
a temperature-dependent free energy using numerical quadrature. This hotQC formulation implements
recently developed optimal summation rules and successfully captures temperature-dependent elastic
constants and thermal expansion. We report for the first time the influence of temperature on force artifacts
and conclude that our novel finite-temperature adaptive nonlocal QC shows minimal force artifacts and
outperforms existing formulations. We also highlight the influence of quadrature in phase space on
simulation outcomes.

We study 3D grain boundaries in the nonlocal hotQC framework (previously limited to single-crystals), by
modeling coarse-grained symmetric-tilt grain boundaries in coincidence site lattice (CSL) based bicrystals.
We predict relaxed energy states of various Σ-boundaries with reasonable accuracy by comparing grain
boundary energies to MD simulations and outline a framework to model polycrystalline materials
that surpass both spatial and temporal limitations of traditional MD.