Related papers: Derivation and study of dynamical models of disloc…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
Plasticity is governed by the evolution of, in general anisotropic, systems of dislocations. We seek to faithfully represent this evolution in terms of density-like variables which average over the discrete dislocation microstructure.…
To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
A phenomenological model of the evolution of an ensemble of interacting dislocations in an isotropic elastic medium is formulated. The line-defect microstructure is described in terms of a spatially coarse-grained order parameter, the…
Crystal plasticity is the result of the motion and interaction of dislocations. There is, however, still a major gap between microscopic and mesoscopic simulations and continuum crystal plasticity models. Only recently a higher dimensional…
In continuum models of dislocations, proper formulations of short-range elastic interactions of dislocations are crucial for capturing various types of dislocation patterns formed in crystalline materials. In this article, the continuum…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
Dislocations are the main carriers of the permanent deformation of crystals. For simulations of engineering applications, continuum models where material microstructures are represented by continuous density distributions of dislocations…
The static stress needed to depin a 2D edge dislocation, the lower dynamic stress needed to keep it moving, its velocity and displacement vector profile are calculated from first principles. We use a simplified discrete model whose far…
In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model…
A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic…
Continuum models of dislocation plasticity require constitutive closure assumptions, e.g., by relating details of the dislocation microstructure to energy densities. Currently, there is no systematic way for deriving or extracting such…
We study the relaxation dynamics of systems of straight, parallel crystal dislocations, starting from initially random and uncorrelated positions of the individual dislocations. A scaling model of the relaxation process is constructed by…
We propose a dynamic version of the three-dimensional translation gauge theory of dislocations. In our approach, we use the notions of the dislocation density and dislocation current tensors as translational field strengths and the…
The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random…
Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or 'curvature density') as an additional…