522 citations · 2.1k across the 73 of their papers we have counts for
4 papers · 1 filter
Energy-Based Atomistic-to-Continuum Coupling Without Ghost Forces
Christoph Ortner, Lei Zhang
We present a practical implementation of an energy-based atomistic-to-continuum (a/c) coupling scheme without ghost forces, and numerical tests evaluating its accuracy relative to…
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
V. Ehrlacher, C. Ortner, A. V. Shapeev
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding t…
Existence and stability of a screw dislocation under anti-plane deformation
Thomas Hudson, Christoph Ortner
We formulate a variational model for a geometrically necessary screw dislocation in an anti-plane lattice model at zero temperature. Invariance of the energy functional under latti…
Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner +1
We formulate an atomistic-to-continuum coupling method based on blending atomistic and continuum forces. Our precise choice of blending mechanism is informed by theoretical predict…