Related papers: Continuum Model and Numerical Method for Dislocati…
Segregation of impurities to grain boundaries plays an important role in both the stability and macroscopic behavior of polycrystalline materials. The research objective in this work is to better characterize the energetics and length…
As a guide to constitutive specification, driving forces for dislocation velocity and nucleation rates are derived for a field theory of dislocation mechanics. A condition of closure for the theory in the form of a boundary condition for…
We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations that compensate the lattice misfit…
In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by…
The emergence of long-range order at low temperatures in atomistic systems with continuous symmetry is a fundamental, yet poorly understood phenomenon in Physics. To address this challenge we study a discrete microscopic model for an…
Modeling deformation twin nucleation in magnesium has proven to be a challenging task. In particular, the absence of a heterogeneous twin nucleation model which provides accurate energetic descriptions for twin-related structures belies a…
Triple junctions, line defects formed by the intersection of different grain boundaries, exist within all polycrystalline materials. While it has long been recognized that triple junctions could play an important role in microstructural…
A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells - a honeycomb pattern.…
A description of dislocations and disclinations defects in terms of Riemann--Cartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
We study the dynamic process occurring when a granular assembly is displaced by a solid impactor. The momentum transfer from the impactor to the target is shown to occur through sporadic, normal collisions of high force carrying grains at…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
A three-dimensional continuum dislocation theory for single crystals containing curved dislocations is proposed. A set of governing equations and boundary conditions is derived for the true placement, plastic slips, and loop functions in…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
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 review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint.…
Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually, constant coefficients of restitution are introduced phenomenologically…
In this paper we present a simple and effective numerical method which allows a fast Fourier transformation-based evaluation of stress generated by dislocations with arbitrary directions and Burgers vectors if the (site-dependent)…
We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…