Related papers: Minimal Surfaces, Screw Dislocations and Twist Gra…
We present a continuum model to determine the dislocation structure and energy of low angle grain boundaries in three dimensions. The equilibrium dislocation structure is obtained by minimizing the grain boundary energy that is associated…
To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For…
According to recent experimental and numerical investigations if the characteristic size of a specimen is in the submicron size regime several new interesting phenomena emerge during the deformation of the samples. Since in such a systems…
Dislocation patterning and self-organization during plastic deformation are associated with work hardening, but the exact mechanisms remain elusive. This is partly because studies of the structure and local strain during the initial stages…
The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On…
The sharp growth of the fracture toughness after brittle-ductile transition happens at grain sizes approximately equal to the plastic zone size. Here we analyze the influence of the grain boundary on the evolution of the ensemble of…
In classical elasticity theory the stress-field of a dislocation is characterized by a $1/r$-type singularity. When such a dislocation is considered together with an Allen-Cahn-type phase-field description for microstructure evolution this…
We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting…
Shear coupling implies that all grain boundary (GB) migration necessarily creates mechanical stresses/strains and is a key component to the evolution of all polycrystalline microstructures. We present MD simulation data and theoretical…
The modest aim of this short article is to provide some new results for a screw dislocation in a functionally graded material within the theory of gradient elasticity. These results, based on a displacement formulation and the Fourier…
Granular materials are known to separate by size under a variety of circumstances. Experiments presented here and elucidated by modeling and MD simulation document a new segregation mechanism, namely segregation by friction. The experiments…
The internal energy associated with the defect microstructure of strongly deformed crystals provides an important driving force for grain boundary motion during recrystallization. Typical dislocation microstructures are strongly…
Fragile topology, akin to twisted bilayer graphene and the exotic phases therein, is a notable topological class with intriguing properties. However, due to its unique nature and the lack of bulk-edge correspondence, the experimental…
In this work we derive conditions that predict the existence of two-phase periodic-pattern grain boundary structures that are stable against coarsening. While previous research has established that elastic effects can lead to phase pattern…
Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface…
We investigate the diffusion of a grain boundary in a crystalline material. We consider in particular the case of a regularly spaced low-angle grain boundary schematized as an array of dislocations that interact with each other through…
We study segregation of granular mixtures in the continuous avalanche regime (for frequencies above ~ 1 rpm) in thin rotating drums using a continuum theory for surface flows of grains. The theory predicts profiles in agreement with…
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…
We discuss how simulations of mechanical properties of materials require descriptions at many different length scales --- from the nanoscale where an atomic description is appropriate, through a mesoscale where dislocation based…
Size-dependence of plastic flow is studied by discrete dislocation dynamical simulation of systems with various numbers of interacting linear edge dislocations while the stress is slowly increased. Regions between avalanches in the…