Related papers: Line and Point Defects in Nonlinear Anisotropic So…
By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are…
A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and…
In this paper we study the wedge disclination within the elastoplastic defect theory. Using the stress function method we found exact analytical solutions for all characteristic fields of a straight wedge disclination in a cylinder. The…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment…
Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By…
Generalizing recent work on isotropic tensor fields in isotropic and achiral condensed matter systems from two to arbitrary dimensions we address both mathematical aspects assuming perfectly isotropic systems and applications focusing on…
The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect…
The aim of this paper is to offer an analytic theory of the shear banding instability in amorphous solids that are subjected to athermal quasi-static shear. To this aim we derive nonlinear equations for the displacement field, including the…
Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This…
The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with…
The incompatibility of linearized piecewise smooth strain field, arising out of volumetric and surface densities of topological defects and metric anomalies, is investigated. First, general forms of compatibility equations are derived for a…
We discuss the theoretical solution to the differential equations governing accelerating edge dislocations in anisotropic crystals. This is an important prerequisite to understanding high speed dislocation motion, including an open question…
Within the continuum dislocation theory the asymptotic analysis of the plane strain crack problem for a single crystal having only one active slip system on each half-plane is provided. The results of this asymptotic analysis show that the…
The strain incompatibility equations are discussed for nonlinear Kirchhoff-Love shells with sources of inhomogeneity arising due to a distribution of topological defects, such as dislocations and disclinations, and metric anomalies, such as…
We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium.…
We investigate the conditions for the (in)stability of the isotropic pressure condition in collapsing spherically symmetric, dissipative fluid distributions. It is found that dissipative fluxes, and/or energy density inhomogeneities and/or…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape?…
It is now well-established that mechanical equilibrium in athermal disordered solids gives rise to anisotropic spatial correlations of the coarse-grained stress field that decay in space as $1/r^d$, where $r$ is the distance from the…
Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is…