29 citations · 100 across the 15 of their papers we have counts for
19 papers
On the linearised force balance condition in the analysis of atomistic dislocation models
Julian Braun, Thomas Hudson
A technical condition arising in the analysis of atomistic models for dislocations is studied. Key estimates for the far-field strain behaviour proved in Ehrlacher, Ortner, Shapeev…
On first-order thermodynamic equilibrium conditions for fluid-fluid and solid-phase interfaces
Nicodemo Di Pasquale, Thomas Hudson
Starting from the constrained variational formulation of Larché and Cahn for solids in contact with fluids, a unified thermodynamic framework for such systems is developed. Both bu…
Simulations of dislocation dynamics on an atomic lattice: the effect of collision rules
Tom Hudson, Akaraphon Jantaraphum, Patrick van Meurs
The stochastic dynamics of dislocations on a one-dimensional periodic lattice domain are considered. Two models are studied: one without a collision rule, and one which annihilates…
Dynamical properties of coarse-grained linear SDEs
Thomas Hudson, Xingjie Helen Li
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. I…
Elasto-plastic evolution of single crystals driven by dislocation flow
Thomas Hudson, Filip Rindler
This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are ent…
Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect
Julian Braun, Thomas Hudson, Christoph Ortner
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…
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…
Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis
Thomas Hudson, Frédéric Legoll, Tony Lelièvre
Motivated by rate-independent stress-strain hysteresis observed in filled rubber, this article considers a scalar viscoelastic model in which the constitutive law is random and var…
Properties of screw dislocation dynamics: time estimates on boundary and interior collisions
Thomas Hudson, Marco Morandotti
In this paper, the dynamics of a system of a finite number of screw dislocations is studied. Under the assumption of antiplane linear elasticity, the two-dimensional dynamics is de…
Asymptotic analysis of boundary layers in a repulsive particle system
Cameron Hall, Thomas Hudson, Patrick van Meurs
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsi…
Upscaling a model for the thermally-driven motion of screw dislocations
Thomas Hudson
We formulate and study a stochastic model for the thermally-driven motion of interacting straight screw dislocations in a cylindrical domain with a convex polygonal cross-section.…
Analysis of stable screw dislocation configurations in an anti--plane lattice model
Thomas Hudson, Christoph Ortner
We consider a variational anti-plane lattice model and demonstrate that at zero temperature, there exist locally stable states containing screw dislocations, given conditions on th…
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…
Gamma-expansion for a 1D Confined Lennard-Jones model with point defect
Thomas Hudson
We compute a rigorous asymptotic expansion of the energy of a point defect in a 1D chain of atoms with second neighbour interactions. We propose the Confined Lennard-Jones model fo…