7 papers
A Systematic Analysis of the Memory term in Coarse-Grained models: the case of the Markovian Approximation
N. Di Pasquale, T. Hudson, M. Icardi +2
The systematic development of Coarse-Grained (CG) models via the Mori-Zwanzig projector operator formalism requires the explicit description of several terms, including a determini…
Atomistic origins of continuum dislocation dynamics
Thomas Hudson, Patrick van Meurs, Mark A. Peletier
This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocati…
Analysis of cell size effects in atomistic crack propagation
Maciej Buze, Thomas Hudson, Christoph Ortner
We consider crack propagation in a crystalline material in terms of bifurcation analysis. We provide evidence that the stress intensity factor is a natural bifurcation parameter, a…
Analysis of an atomistic model for anti-plane fracture
Maciej Buze, Thomas Hudson, Christoph Ortner
We develop a model for an anti-plane crack defect posed on a square lattice under an interatomic pair-potential with nearest-neighbour interactions. In particular, we establish exi…
An existence result for Discrete Dislocation Dynamics in three dimensions
Thomas Hudson
We present a mathematical framework within which Discrete Dislocation Dynamics in three dimensions is well-posed. By considering smooth distributions of slip, we derive a regularis…
Systematic derivation of hybrid coarse-grained models
Nicodemo Di Pasquale, Thomas Hudson, Matteo Icardi
Significant efforts have been devoted in the last decade towards improving the predictivity of coarse-grained models in molecular dynamics simulations and providing a rigorous just…