Related papers: Self-energy of dislocations and dislocation pileup…
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)…
We propose an energy-consistent mathematical model for motion of dislocation curves in elastic materials using the idea of phase field model. This reveals a hidden gradient flow structure in the dislocation dynamics. The model is derived as…
This paper develops the small strain continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening for single crystals. As illustration, the problem of anti-plane constrained shear of single crystal…
We derive a continuum-level plasticity model for polycrystalline materials in the high energy density regime, based on a single dislocation density and single mobility mechanism, with an evolution model for the dislocation density. The…
Dynamic nucleation of dislocations caused by a stress front ('shock') of amplitude $\sigma_{\rm a}$ moving with speed $V$ is investigated by solving numerically the Dynamic Peierls Equation with an efficient method. Speed $V$ and amplitude…
Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in…
For a given external loading on a structure we consider the optimal stresses. Ignoring the material properties the structure may have, we look for the distribution of internal forces or stresses that is in equilibrium with the external…
In seeking to understand at a microscopic level the response of dislocations to stress we have undertaken to study as completely as possible the simplest case: a single dislocation in a two dimensional crystal. The intention is that results…
A novel model based on the Peierls framework of dislocations is developed. The new theory can deal with a dislocation spreading at more than one slip planes. As an example, we study dislocation cross-slip and constriction process of two fcc…
Equilibrium statistical mechanics tools have been developed to obtain indications about the natural tendencies of nonlinear energy transfers in two-dimensional and quasi two-dimensional flows like rotating and stratified flows in…
We prove Taylor scaling for dislocation lines characterized by line-tension and moving by curvature under the action of an applied shear stress in a plane containing a random array of obstacles. Specifically, we show--in the sense of…
Self-organization of active matter as well as driven granular matter in non-equilibrium dynamical states has attracted considerable attention not only from the fundamental and application viewpoints but also as a model to understand the…
In view of the fundamental distinction between the force-controlled model and the displacement-controlled model in buckling problems of structures and the complexity of the asymptotic post-buckling analysis traditionally based on the…
We present results of molecular simulations of a model protein whose hydrophobic collapse proceeds as a cascade of downhill transitions between distinct intermediate states. Different intermediates are stabilized by means of appropriate…
The energy of a dislocation loop in a continuum elastic solid under pressure is considered within the framework of classical mechanics. For a circular loop, this is a function with a maximum at pressures that are well within reach of…
We study dislocation networks in the plane using the vectorial phase-field model introduced by Ortiz and coworkers, in the limit of small lattice spacing. We show that, in a scaling regime where the total length of the dislocations is…
We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy,…
We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment…
The current interest in compositionally complex alloys including so called high entropy alloys has caused renewed interest in the general problem of solute hardening. It has been suggested that this problem can be addressed by treating the…
We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models…