13,426 research outputs found
Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress
This paper deals with the parallel simulation of delamination problems at the
meso-scale by means of multi-scale methods, the aim being the Virtual
Delamination Testing of Composite parts. In the non-linear context, Domain
Decomposition Methods are mainly used as a solver for the tangent problem to be
solved at each iteration of a Newton-Raphson algorithm. In case of strongly
nonlinear and heterogeneous problems, this procedure may lead to severe
difficulties. The paper focuses on methods to circumvent these problems, which
can now be expressed using a relatively general framework, even though the
different ingredients of the strategy have emerged separately. We rely here on
the micro-macro framework proposed in (Ladev\`eze, Loiseau, and Dureisseix,
2001). The method proposed in this paper introduces three additional features:
(i) the adaptation of the macro-basis to situations where classical
homogenization does not provide a good preconditioner, (ii) the use of
non-linear relocalization to decrease the number of global problems to be
solved in the case of unevenly distributed non-linearities, (iii) the
adaptation of the approximation of the local Schur complement which governs the
convergence of the proposed iterative technique. Computations of delamination
and delamination-buckling interaction with contact on potentially large
delaminated areas are used to illustrate those aspects
Asymptotic wave-splitting in anisotropic linear acoustics
Linear acoustic wave-splitting is an often used tool in describing sound-wave
propagation through earth's subsurface. Earth's subsurface is in general
anisotropic due to the presence of water-filled porous rocks. Due to the
complexity and the implicitness of the wave-splitting solutions in anisotropic
media, wave-splitting in seismic experiments is often modeled as isotropic.
With the present paper, we have derived a simple wave-splitting procedure for
an instantaneously reacting anisotropic media that includes spatial variation
in depth, yielding both a traditional (approximate) and a `true amplitude'
wave-field decomposition. One of the main advantages of the method presented
here is that it gives an explicit asymptotic representation of the linear
acoustic-admittance operator to all orders of smoothness for the smooth,
positive definite anisotropic material parameters considered here. Once the
admittance operator is known we obtain an explicit asymptotic wave-splitting
solution.Comment: 20 page
Scale effects in orthotropic composite assemblies as micropolar continua: A comparison between weak-and strong-form finite element solutions
The aim of the present work was to investigate the mechanical behavior of orthotropic
composites, such as masonry assemblies, subjected to localized loads described as micropolar
materials. Micropolar models are known to be effective in modeling the actual behavior of
microstructured solids in the presence of localized loads or geometrical discontinuities. This is
due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic
model, if compared to the classical continuum and the related strain and stress measures. In particular,
it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar
continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic
response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein.
Numerical simulations are provided by comparing weak and strong finite element formulations.
The scale effect is investigated, as well as the significant role played by the relative rotation,
which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and
work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli,
related to the variation of microstructure internal sizes, are highlighted
Modeling anisotropic diffusion using a departure from isotropy approach
There are a large number of finite volume solvers available for solution of isotropic diffusion equation. This article presents an approach of adapting these solvers to solve anisotropic diffusion equations. The formulation works by decomposing the diffusive flux into a component associated with isotropic diffusion and another component associated with departure from isotropic diffusion. This results in an isotropic diffusion equation with additional terms to account for the anisotropic effect. These additional terms are treated using a deferred correction approach and coupled via an iterative procedure. The presented approach is validated against various diffusion problems in anisotropic media with known analytical or numerical solutions. Although demonstrated for two-dimensional problems, extension of the present approach to three-dimensional problems is straight forward. Other than the finite volume method, this approach can be applied to any discretization method
Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media
In this paper we propose and analyze a preconditioner for a system arising
from a finite element approximation of second order elliptic problems
describing processes in highly het- erogeneous media. Our approach uses the
technique of multilevel methods and the recently proposed preconditioner based
on additive Schur complement approximation by J. Kraus (see [8]). The main
results are the design and a theoretical and numerical justification of an
iterative method for such problems that is robust with respect to the contrast
of the media, defined as the ratio between the maximum and minimum values of
the coefficient (related to the permeability/conductivity).Comment: 28 page
Modelling of Phase Separation in Alloys with Coherent Elastic Misfit
Elastic interactions arising from a difference of lattice spacing between two
coherent phases can have a strong influence on the phase separation
(coarsening) of alloys. If the elastic moduli are different in the two phases,
the elastic interactions may accelerate, slow down or even stop the phase
separation process. If the material is elastically anisotropic, the
precipitates can be shaped like plates or needles instead of spheres and can
form regular precipitate superlattices. Tensions or compressions applied
externally to the specimen may have a strong effect on the shapes and
arrangement of the precipitates. In this paper, we review the main theoretical
approaches that have been used to model these effects and we relate them to
experimental observations. The theoretical approaches considered are (i)
`macroscopic' models treating the two phases as elastic media separated by a
sharp interface (ii) `mesoscopic' models in which the concentration varies
continuously across the interface (iii) `microscopic' models which use the
positions of individual atoms.Comment: 106 pages, in Latex, figures available upon request, e-mail
addresses: [email protected], [email protected],
[email protected], submitted to the Journal of Statistical Physic
Wave splitting of Maxwell's equations with anisotropic heterogeneous constitutive relations
The equations for the electromagnetic field in an anisotropic media are
written in a form containing only the transverse field components relative to a
half plane boundary. The operator corresponding to this formulation is the
electromagnetic system's matrix. A constructive proof of the existence of
directional wave-field decomposition with respect to the normal of the boundary
is presented.
In the process of defining the wave-field decomposition (wave-splitting), the
resolvent set of the time-Laplace representation of the system's matrix is
analyzed. This set is shown to contain a strip around the imaginary axis. We
construct a splitting matrix as a Dunford-Taylor type integral over the
resolvent of the unbounded operator defined by the electromagnetic system's
matrix. The splitting matrix commutes with the system's matrix and the
decomposition is obtained via a generalized eigenvalue-eigenvector procedure.
The decomposition is expressed in terms of components of the splitting matrix.
The constructive solution to the question on the existence of a decomposition
also generates an impedance mapping solution to an algebraic Riccati operator
equation. This solution is the electromagnetic generalization in an anisotropic
media of a Dirichlet-to-Neumann map.Comment: 45 pages, 2 figure
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