4 papers · 1 filter
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 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…
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…