Search results for "boundary"

Formation of surface roughness on nanocrystalline aluminum samples under straining by molecular dynamics studies

2006

International audience; The surface roughening of nanocrystalline aluminum samples was investigated by molecular dynamics simulations. Attention was focused on the fact that roughness increases with the grain size and the strain. The elastic-plastic transition was found at around 3.5% strain and a reverse Hall-Petch effect was observed under straining conditions. Then, different strain distributions in grains and grain boundaries at the samples surface was highlighted, yielding to the formation of local roughness. Finally, a linear relationship between the magnitude of roughness and the out-of-plane strain component was found.

Micro-cracking of brittle polycrystalline materials with initial damage

2016

In this paper, the effect of pre-existing damage on brittle micro-cracking of polycrystalline materials is explored. The behaviour of single and multiple cracks randomly distributed within a grain scale polycrystalline aggregate is investigated using a recently developed grain boundary 3D computational framework. Each grain is modelled as a single crystal anisotropic domain. Opening, sliding and/or contact at grain boundaries are modelled using nonlinear cohesive-frictional laws. The polycrystalline micro-morphologies are generated using Voronoi tessellation algorithms in combination with a regularisation scheme to avoid the presence of unnecessary small geometrical entities (edges and face…

On the convergence of the finite element approximation of eigenfrequencies and eigenvectors to Maxwell's boundary value problem

1981

A Variational Approach to Boundary Element Methods

1988

Interlaminar stresses in laminated composite beam-type structures under shear/bending

2000

A boundary integral model for composite laminates under out-of-plane shear/bending is presented. The formulation proposed allows one to determine the elastic response of generally stacked composite laminates having general shape of the cross section. The integral equations governing the ply behavior within the laminate are deduced starting from the reciprocity theorem for beam-type structures. The ply integral equations are obtained by employing the analytical expression of the fundamental solution of generalized plane strain anisotropic problems. The laminate model is completed by imposing the displacement and stress continuity along the interfaces and the external boundary conditions. The…

A non-local model of fractional heat conduction in rigid bodies

2011

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent s…

Regularization and finite element approximation of the wave equation with Dirichlet boundary data

1990

Types and Multiplicity of Solutions to Sturm–Liouville Boundary Value Problem

2015

We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.

Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers.

2004

Translation Matrix Formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional (1D) periodic stratified structure. This modal approach allows to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to Second Harmonic Generation (SHG) in the undepleted pump regime.

Navier-Stokes equations on an exterior circular domain: construction of the solution and the zero viscosity limit

1997

Abstract In this Note, we consider the limit of Navier-Stokes equations on a circular domain. By an explicit construction of the solution, it is proved that, when viscosity goes to zero, solution converges to the Euler solution outside the boundary layer and to the Prandtl solution inside the boundary layer.