Related papers: Minimal Surfaces, Screw Dislocations and Twist Gra…
Theoretical calculations of the structure, formation and migration of kinks on a non-dissociated screw dislocation in silicon have been carried out using density functional theory calculations as well as calculations based on interatomic…
The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of yielding transitions and grain-size effects in polycrystalline solids. Calculations are based on the 1995 experimental results of…
We demonstrate insights into the three-dimensional structure of defects in graphene, in particular grain boundaries, obtained via a new approach from two transmission electron microscopy images recorded at different angles. The structure is…
Stretching, drilling, and bending are the independent deformation modes of a thin shell, each of which has an individual energy content. When the energy content of a mode vanishes, that mode is neutral. We characterize all neutral modes of…
A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in Ref. [48]. The model is based on the motion and reaction of the constituent…
Using a recently developed continuum theory of dislocation dynamics, we derive three new predictions about plasticity and grain boundary formation in crystals. (1) There will be a residual stress jump across grain boundaries and…
Strain and rotation fields of dislocations in monolayer graphene have been mapped in a recent experiment. These fields are finite everywhere and differ from those given by linear elasticity which does not consider rotation explicitly and…
Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion…
The twist-grain-boundary (TGB) phases, characterized by a periodic, helical arrangement of blocks made of polar smectic phases, SmAF and SmCF, have been discovered. They have been observed for rod-like molecules with a strong longitudinal…
The strain incompatibility equations are discussed for nonlinear Kirchhoff-Love shells with sources of inhomogeneity arising due to a distribution of topological defects, such as dislocations and disclinations, and metric anomalies, such as…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
We have characterized the structure of 176 different single-layer graphene grain boundaries using $>$1000 experimental HRTEM images using a semi-automated structure processing routine. We introduce a new algorithm for generating grain…
We first report a detailed transmission electron microscopy study of dislocation networks (DNs) formed at shallowly buried interfaces obtained by bonding two GaAs crystals between which we establish in a controlled manner a twist and a tilt…
Dislocations in perovskite oxides have important impacts on their physical and chemical properties, which are determined by their unique atomic environments. In the present study, the structure of dislocations in a 10{\deg} low-angle grain…
Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the…
We study the structural features and underlying principles of multi-dislocation ground states of a crystalline spherical cap. In the continuum limit where the ratio of crystal size to lattice spacing $W/a$ diverges, dislocations proliferate…
Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local…
Dislocation dynamics simulation is used to investigate the effect of grain size and grain shape on the flow stress in model copper grains. We consider grains of 1.25-10 $\mu$m size, three orientations (<135>, <100> and <111>) and three…
We describe the geometry of bend distortions in twist-bend nematic liquid crystals in terms of their fundamental degeneracies, which we call $\beta$ lines. These represent a new class of line-like topological defect. We use them to…
Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters…