Related papers: Self-energy of dislocations and dislocation pileup…
This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the…
We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two…
We study a one-dimensional model of a dislocation pileup driven by an external stress and interacting with random quenched disorder, focusing on predictability of the plastic deformation process. Upon quasistatically ramping up the…
The distribution of internal shear stresses in a 2D dislocation system is investigated when external shear stress is applied. This problem serves as a natural continuation of the previous work of Csikor and Groma (Csikor F F and Groma I…
We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low angle grain boundaries interacting with a disordered stress landscape provided by solute…
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…
In this work we study a charged particle in the presence of both a continuous distribution of disclinations and a continuous distribution of edge dislocations in the framework of the geometrical theory of defects. We obtain the self-energy…
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…
Dislocation dynamic is a typically gradient flow problem, and most of work solves it just as ODE, which means that the interacting energy of dislocations is ignored. We take the interaction energy into account and use it to introduce new…
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…
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…
Due to recent successes of a statistical-based nonlocal continuum crystal plasticity theory for single-glide in explaining various aspects such as dislocation patterning and size-dependent plasticity, several attempts have been made to…
In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation…
A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material…
In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…
An asymptotically exact continuum dislocation theory of single crystal bars under torsion is proposed. The dislocation distribution minimizing energy of the bar with zero torque is shown to be uniform. If the applied torque is non-zero, the…
We present a variational theory for lattice defects of rotational and translational type. We focus on finite systems of planar wedge disclinations, disclination dipoles, and edge dislocations, which we model as the solutions to minimum…
Relaxation processes of dislocation systems are studied by two-dimensional dynamical simulations. In order to capture generic features, three physically different scenarios were studied and power-law decays found for various physical…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
Anti-plane shear deformations of a hexagonal quasi-crystal with multiple screw dislocations are considered. Using a variational formulation, the elastic equilibrium is characterized via limit of minimizers of a core-regularized energy…