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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…
We provide a comprehensive theoretical framework to study how crystal dislocations influence the functional properties of materials, based on the idea of quantized dislocation, namely a "dislon". In contrast to previous work on dislons…
The stability to dislocations of the elastic phase, or ``Bragg glass'', of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully-packed loop model. The elastic phase is…
The primary factors controlling defect stability in phase-field crystal (PFC) models are examined, with illustrative examples involving several existing variations of the model. Guidelines are presented for constructing models with stable…
We study a one-dimensional model of a dislocation pileup driven by an external stress and interacting with random quenched disorder, focusing on predictability of the plastic deformation process. Upon quasistatically ramping up the…
Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show,…
We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…
Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli…
We generalize, and then use, a recently introduced formalism to study thermal fluctuations of atomic displacements in several two and three dimensional crystals. We study both close packed as well as open crystals with multi atom bases.…
A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
Materials are often heterogeneous at various length scales, with variations in grain structure, defects, and composition which has a strong influence on the emergent macroscopic plastic behavior. In particular, heterogeneities lead to…
Dislocations in soft condensed matter systems such as lamellar systems of polymers, liquid crystals and ternary mixtures of oil, water and surfactant (amphiphilic systems) are described in the framework of continuum elastic theory. These…
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…
Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are…
The fact that a disordered material is not constrained in its properties in the same way as a crystal presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts,…
The yield surface in crystal plasticity can be approached from various directions during mechanical loading. We consider the competition between nanoindentation and tensile loading towards plastic yielding. For this purpose, we develop a…
The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various point-like defects such as precipitates or solute atoms. These…
The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…