Related papers: On the Structure of Linear Dislocation Field Theor…
We rigorously derive a strain-gradient model of plasticity as a $\Gamma$-limit of continuum bodies containing finitely-many edge-dislocations (in two dimensions). The key difference from previous such derivations is the elemental notion of…
Plastic deformation in microscale differs from the macroscopic plasticity in two respects: (i) the flow stress of small samples depends on their size (ii) the scatter of plasticity increases significantly. In this work we focus on the…
The existence of stress singularities and reliance on linear approximations pose significant challenges in comprehending the stress field generation mechanism around dislocations. This study employs differential geometry and calculus of…
We present a framework which unifies classical phenomenological $J_2$ and crystal plasticity theories with quantitative dislocation mechanics. The theory allows the computation of stress fields of arbitrary dislocation distributions and,…
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…
In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…
The aim of this paper is to investigate the numerical implementation of the Field Dislocation Mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006) is…
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…
In this paper we study the twist disclination within the elastoplastic defect theory. Using the stress function method, we found exact analytical solutions for all characteristic fields of a straight twist disclination in an infinitely…
Progress toward a first-principles theory of plasticity and work-hardening is currently impeded by an insufficient picture of dislocation kinetics (the dynamic effect of driving forces in a given dislocation theory). This is because present…
This paper develops the small strain continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening for single crystals. As illustration, the problem of anti-plane constrained shear of single crystal…
A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress…
The static stress needed to depin a 2D edge dislocation, the lower dynamic stress needed to keep it moving, its velocity and displacement vector profile are calculated from first principles. We use a simplified discrete model whose far…
In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation…
The present paper extends the thermodynamic dislocation theory developed by Langer, Bouchbinder, and Lookmann to non-uniform plastic deformations. The free energy density as well as the positive definite dissipation function are proposed.…
A generalized disclination (g.disclination) theory [AF15] has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of…
The fundamental problem of non-singular dislocations in the framework of the theory of gradient elasticity is presented in this work. Gradient elasticity of Helmholtz type and bi-Helmholtz type are used. A general theory of non-singular…
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…
This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…
Dislocations are topological defects known to be crucial in the onset of plasticity and in many properties of crystals. Classical Elasticity still fails to fully explain their dynamics under extreme conditions of high strain gradients and…