Related papers: On the Structure of Linear Dislocation Field Theor…

A field theory is developed for a thermodynamical description of array of parallel non-singular screw dislocations in elastic cylinder. The partition function of the system is considered in the functional integral form. Self-energy of the…

We investigate the nonuniform motion of a straight screw dislocation in infinite media in the framework of the translational gauge theory of dislocations. The equations of motion are derived for an arbitrary moving screw dislocation. The…

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…

We propose a numerical model to study the viscoplastic deformation of ice single crystals. We consider long-range elastic interactions among dislocations, the possibility of mutual annihilation, and a multiplication mechanism representing…

We propose a discrete lattice model of the energy of dislocations in three-dimensional crystals which properly accounts for lattice symmetry and geometry, arbitrary harmonic interatomic interactions, elastic deformations and discrete…

We show that certain mixed displacement/traction problems (including live pressure tractions) of nonlinear elastostatics that are solved by a homogeneous deformation, admit no other classical equilibrium solution under suitable constitutive…

The present work is essentially concerned with the development of statistical theory for the low temperature dislocation glide in concentrated solid solutions where atom-sized obstacles impede plastic flow. In connection with such a…

This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…

We develop a non-singular theory of three-dimensional dislocation loops in a particular version of Mindlin's anisotropic gradient elasticity with up to six length scale parameters. The theory is systematically developed as a generalization…

We study strain-controlled plastic deformation of crystalline solids via two-dimensional discrete dislocation dynamics simulations. To this end, we characterize the average stress-strain curves as well as the statistical properties of…

This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation lines. The model is geometrically and elastically nonlinear,…

We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The…

Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport…

We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.

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…

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 entirely driven by the movement of dislocations, that is,…

We use a discrete dislocation dynamics (DDD) approach to study the motion of a dislocation under strong stochastic forces that may cause bending and roughening of the dislocation line on scales that are comparable to the dislocation core…

A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy…

This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…

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…