Mesoscopic and multiscale modelling in materials
The concept of multiscale modelling has emerged over the last few decades to describe
procedures that seek to simulate continuum-scale behaviour using information gleaned from …
procedures that seek to simulate continuum-scale behaviour using information gleaned from …
A review of local-to-nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
Abstract Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining
nonlocal and local modeling descriptions of a given system into a unified coupled …
nonlocal and local modeling descriptions of a given system into a unified coupled …
Molecular dynamics
For a number of years, we have been exploring the underpinnings of algorithms for
simulating molecular dynamics from a mathematics perspective, ie as outsiders. We have …
simulating molecular dynamics from a mathematics perspective, ie as outsiders. We have …
[HTML][HTML] A theoretical case study of the generalization of machine-learned potentials
Abstract Machine-learned interatomic potentials (MLIPs) are typically trained on datasets
that encompass a restricted subset of possible input structures, which presents a potential …
that encompass a restricted subset of possible input structures, which presents a potential …
Analysis of boundary conditions for crystal defect atomistic simulations
Numerical simulations of crystal defects are necessarily restricted to finite computational
domains, supplying artificial boundary conditions that emulate the effect of embedding the …
domains, supplying artificial boundary conditions that emulate the effect of embedding the …
A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions
We develop and analyze an optimization-based method for the coupling of nonlocal and
local diffusion problems with mixed volume constraints and boundary conditions. The …
local diffusion problems with mixed volume constraints and boundary conditions. The …
A framework for a generalization analysis of machine-learned interatomic potentials
Machine-learned interatomic potentials (MLIPs) and force fields (ie, interaction laws for
atoms and molecules) are typically trained on limited data-sets that cover only a very small …
atoms and molecules) are typically trained on limited data-sets that cover only a very small …
A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals
In recent years, numerous partitioned-domain methods have been developed to describe
dislocation behavior at length scales that are usually inaccessible to most classical atomistic …
dislocation behavior at length scales that are usually inaccessible to most classical atomistic …
Justification of the Cauchy–Born approximation of elastodynamics
C Ortner, F Theil - Archive for Rational Mechanics and Analysis, 2013 - Springer
Justification of the Cauchy–Born Approximation of Elastodynamics Page 1 Digital Object
Identifier (DOI) 10.1007/s00205-012-0592-6 Arch. Rational Mech. Anal. 207 (2013) 1025–1073 …
Identifier (DOI) 10.1007/s00205-012-0592-6 Arch. Rational Mech. Anal. 207 (2013) 1025–1073 …
Landau-type theory of planar crystal plasticity
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in
crystals if it is viewed as a Landau theory with an infinite number of equivalent energy wells …
crystals if it is viewed as a Landau theory with an infinite number of equivalent energy wells …