Related papers: Variational approach in dislocation theory

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

In this paper we present the equations of motion of a moving screw dislocation in the framework of the translation gauge theory of dislocations. In the gauge field theoretical formulation, a dislocation is a massive gauge field. We…

The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…

Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds…

The current interest in compositionally complex alloys including so called high entropy alloys has caused renewed interest in the general problem of solute hardening. It has been suggested that this problem can be addressed by treating the…

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…

This paper considers stochastic hybrid stress quadrilateral finite element analysis of plane elasticity equations with stochastic Young's modulus and stochastic loads. Firstly, we apply Karhunen-Lo$\grave{e}$ve expansion to stochastic…

The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…

In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…

We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…

Elucidating the interplay of defect and stress at the microscopic level is a fundamental physical problem that has strong connection with materials science. Here, based on the two-dimensional crystal model, we show that the instability mode…

A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.

The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to…

The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…

The thermally activated motion of dislocations across fields of obstacles distributed at random and in a correlated manner, in separate models, is studied by means of computer simulations. The strain rate sensitivity and strength are…

We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…

The work described here shows that the known variational principle for the Navier-Stokes equations and the adjoint system can be modified to produce a set of Euler-Lagrange variational equations which have the same order and same solution…

We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from…

In this article a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary…

We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law.…