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In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called Composite Finite Elements are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete homogenization...
The minimization of nonconvex functionals naturally arises in
materials sciences where deformation gradients in certain alloys exhibit
microstructures. For example, minimizing sequences of the nonconvex
Ericksen-James energy can be associated with deformations in
martensitic materials that
are observed in experiments[2,3].
— From the numerical
point of view, classical conforming and nonconforming finite element
discretizations have been observed to give minimizers
with their quality being highly
dependent...
The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.
We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.
We present the combination of a state control and shape design approaches
for the optimization of micro-fluidic channels used for sample extraction and
separation of chemical species existing in a buffer solution.
The aim is to improve the extraction and identification capacities of
electroosmotic micro-fluidic devices by avoiding dispersion of the
extracted advected band.
A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms , ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how and can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated...
In the present work an extension of a classical Menabrea’s theorem on a variational principle of the second potential energy is considered. Such extension deals with hyperelastic micropolar media without constraints.
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