Related papers: Variational approach in dislocation theory
We propose a numerical procedure to solve an inverse problem that estimates the state of a magma reservoir from observed surface displacement of a volcano. Our variational approach aims to find the minimizer of a cost function consisting of…
We show how to "concatenate" variational principles over different bases into one over a single base, thereby providing a unified Lagrangian treatment of interacting systems. As an example we study a Klein-Gordon field interacting with a…
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the…
An action functional is developed for nonlinear dislocation dynamics. This serves as a first step towards the application of effective field theory in physics to evaluate its potential in obtaining a macroscopic description of dislocation…
In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven…
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…
Dislocation dynamic is a typically gradient flow problem, and most of work solves it just as ODE, which means that the interacting energy of dislocations is ignored. We take the interaction energy into account and use it to introduce new…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
We present a general formalism for incorporating dislocations in Phase Field methods. This formalism is based on the elastic equivalence between a dislocation loop and a platelet inclusion of specific stress-free strain related to the loop…
A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the…
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…
A differential geometric approach to singular perturbation theory is presented. It is shown that singular perturbation problems such as multiple-scale and boundary layer problems can be treated more easily on a differential geometric basis.…
Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…
We study waves in a rod of finite length with a viscoelastic constitutive equation of fractional distributed-order type for the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain case…
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…
A translational gauge approach of the Einstein type is proposed for obtaining the stresses that are due to non-singular screw dislocation. The stress distribution of second order around the screw dislocation is classically known for the…
In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…
Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…
A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…
In this article we study a coupled system of differential equations with Allen-Cahn type non-linearity. Motivated by physical phenomena one of the unknowns in the system is accompanied by a singular perturbation parameter ${\epsilon}^2$ .…