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We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian %This model describes the evolution of phase transitions associated to dislocations. whose solution represents the atom dislocation in…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
Continuum dislocation dynamics (CDD) has become the state-of-the-art theoretical approach for mesoscale dislocation plasticity of metals. Within this approach, there are multiple CDD theories that can all be derived from the principles of…
To understand how dislocations form ordered structures during the deformation of metals, we perform computer simulation studies of the dynamics and patterning of screw dislocations in two dimensions. The simulation is carried out using an…
In engineering crystal plasticity inelastic mechanisms correspond to tensorial zero-energy valleys in the space of macroscopic strains. The flat nature of such valleys is in contradiction with the fact that plastic slips, mimicking…
A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain…
A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to…
A clear understanding of the dynamic behavior of metals is critical for developing superior structural materials as well as for improving material processing techniques such as cold spray and shot peening. Using a high velocity (from 120…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of screw dislocation in smectic A is the key in which the correct result is just obtained by overcoming a longstanding puzzle [19]. We…
A general procedure to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase field crystal (PFC) models, is presented. It is found…
A phenomenological model of the evolution of an ensemble of interacting dislocations in an isotropic elastic medium is formulated. The line-defect microstructure is described in terms of a spatially coarse-grained order parameter, the…
Collective motion of dislocations is governed by the obstacles they encounter. In pure crystals, dislocations form complex structures as they become jammed by their anisotropic shear stress fields. On the other hand, introducing disorder to…
Dislocations, line defects in crystalline materials, play an essential role in the mechanical[1,2], electrical[3], optical[4], thermal[5], and phase transition[6] properties of these materials. Dislocation motion, an important mechanism…
Crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations are jammed within their glide plane due to long-range elastic interactions and the material exhibits plastic…
In recent years there has been renewed interest in the behavior of dislocations in crystals that exhibit strong atomic scale disorder, as typical of compositionally complex single phase alloys. The behavior of dislocations in such crystals…
The kinetics of dislocations is studied with computer simulation at loadings of different intensity. It is established that the dislocations have a few different structural states. The dislocations "with the micropore" play important role…
Crystal dislocation dynamics, especially at high temperatures, represents a subject where experimental phenomenological input is commonly required, and parameter-free predictions, starting from quantum methods, have been beyond reach. This…
The statistics and origin of the first discrete plastic event in a one dislocation dynamics simulation are studied. This is done via a linear stability analysis of the evolving dislocation configuration up to the onset of irreversible…
Driven by the growing interest in numerical simulations of dislocation-interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple…