相关论文: Field Dislocation Mechanics, Conservation of Burge…
We focus on existence and rigidity problems of the vectorial Peierls-Nabarro (PN) model for dislocations. Under the assumption that the misfit potential on the slip plane only depends on the shear displacement along the Burgers vector, a…
Plastic deformation of crystals is a physical phenomenon, which has immensely driven the development of human civilisation since the onset of the Chalcolithic period. This process is primarily governed by the motion of line defects, called…
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…
We review the continuous theory of dislocations from a mathematical point of view using mathematical tools, which were only partly available when the theory was developed several decades ago. We define a space of dislocation measures, which…
In the modeling of dislocations one is lead naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may…
In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study two cases: i) the particular case of parallel straight…
In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model…
In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core structure. We focus on the static and dynamic PN models of an…
Plasticity of metals is the emergent phenomenon of many crystal defects (dislocations) which interact and move on microscopic time and length scales. Two of the commonly used models to describe such dislocation dynamics are the…
We propose a model to study the plasticity of ice single crystals by numerical simulations. The model includes the long-range character of the interaction among dislocations, as well as the possibility of mutual annihilation of these line…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
A novel semidiscrete Peierls-Nabarro model is introduced which can be used to study dislocation spreading at more than one slip planes, such as dislocation cross-slip and junctions. The strength of the model, when combined with ab initio…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
The utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects like defected grain and phase boundaries, dislocations and disclinations. The…
Incomplete stacking dislocations are predicted to form at edges of the shorter upper layer in two-dimensional hexagonal bilayers upon stretching the longer bottom layer. A concept of the edge Burgers vector is introduced to describe such…
The deformation behaviour of the intermetallic Al$_{2}$Cu-phase was investigated using atomistic simulations and micropillar compression, where slip on the unexpected {211} and {022} slip planes was revealed. Additionally, all possible slip…
This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The…
Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the motion of discrete dislocations, this work performs a rigorous…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
Dislocation core properties of tin (\beta-Sn) were investigated using the semi-discrete variational Peierls-Nabarro model (SVPN). The SVPN model, which connects the continuum elasticity treatment of the long-range strain field around a…