Atomistic-to-continuum coupling
Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale
schemes that combine the accuracy of atomistic models with the efficiency of continuum …
schemes that combine the accuracy of atomistic models with the efficiency of continuum …
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 …
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 …
A machine-learning aided multiscale homogenization model for crystal plasticity: application for face-centered cubic single crystals
Quantitative prediction on mesoscale crystal plasticity via first principle-based methods or
first principle-based multiscale methods is still unreachable, even though several …
first principle-based multiscale methods is still unreachable, even though several …
Formulation and optimization of the energy-based blended quasicontinuum method
We formulate an energy-based atomistic-to-continuum coupling method based on blending
the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results …
the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results …
QM/MM methods for crystalline defects. Part 2: Consistent energy and force-mixing
We develop and analyze QM/MM (quantum/classic) hybrid methods for crystalline defects
within the context of the tight-binding model. QM/MM methods employ accurate quantum …
within the context of the tight-binding model. QM/MM methods employ accurate quantum …
Geometry equilibration of crystalline defects in quantum and atomistic descriptions
We develop a rigorous framework for modeling the geometry equilibration of crystalline
defects. We formulate the equilibration of crystal defects as a variational problem on a …
defects. We formulate the equilibration of crystal defects as a variational problem on a …
Asymptotic expansion of the elastic far-field of a crystalline defect
Lattice defects in crystalline materials create long-range elastic fields which can be
modelled on the atomistic scale using an infinite system of discrete nonlinear force balance …
modelled on the atomistic scale using an infinite system of discrete nonlinear force balance …
Accuracy of quasicontinuum approximations near instabilities
The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries,
occurs when the lattice configuration loses stability, that is, when an eigenvalue of the …
occurs when the lattice configuration loses stability, that is, when an eigenvalue of the …
Analysis of blended atomistic/continuum hybrid methods
We present a comprehensive error analysis of two prototypical atomistic-to-continuum
coupling methods of blending type: the energy-based and the force-based quasicontinuum …
coupling methods of blending type: the energy-based and the force-based quasicontinuum …