121 research outputs found
Quasistatic evolution of a brittle thin film
This paper deals with the quasistatic crack growth of a homogeneous elastic
brittle thin film. It is shown that the quasistatic evolution of a
three-dimensional cylinder converges, as its thickness tends to zero, to a
two-dimensional quasistatic evolution associated with the relaxed model.
Firstly, a -convergence analysis is performed with a surface energy
density which does not provide weak compactness in the space of Special
Functions of Bounded Variation. Then, the asymptotic analysis of the
quasistatic crack evolution is presented in the case of bounded solutions that
is with the simplifying assumption that every minimizing sequence is uniformly
bounded in .Comment: 43 page
Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination
This work is devoted so show the appearance of different cracking modes in
linearly elastic thin film systems by means of an asymptotic analysis as the
thickness tends to zero. By superposing two thin plates, and upon suitable
scaling law assumptions on the elasticity and fracture parameters, it is proven
that either debonding or transverse cracks can emerge in the limit. A model
coupling debonding, transverse cracks and delamination is also discussed
Homogenization of variational problems in manifold valued Sobolev spaces
Homogenization of integral functionals is studied under the constraint that
admissible maps have to take their values into a given smooth manifold. The
notion of tangential homogenization is defined by analogy with the tangential
quasiconvexity introduced by Dacorogna, Fonseca, Maly and Trivisa \cite{DFMT}.
For energies with superlinear or linear growth, a -convergence result
is established in Sobolev spaces, the homogenization problem in the space of
functions of bounded variation being the object of \cite{BM}.Comment: 22 page
Multiscale nonconvex relaxation and application to thin films
-convergence techniques are used to give a characterization of the
behavior of a family of heterogeneous multiple scale integral functionals.
Periodicity, standard growth conditions and nonconvexity are assumed whereas a
stronger uniform continuity with respect to the macroscopic variable, normally
required in the existing literature, is avoided. An application to dimension
reduction problems in reiterated homogenization of thin films is presented.Comment: 40 pages, 5 figure
3D-2D analysis of a thin film with periodic microstructure
The purpose of this article is to study the behavior of a heterogeneous thin
film whose microstructure oscillates on a scale that is comparable to that of
the thickness of the domain. The argument is based on a 3D-2D dimensional
reduction through a -convergence analysis, techniques of two-scale
convergence and a decoupling procedure between the oscillating variable and the
in-plane variable.Comment: 19 page
Hyperbolic structure for a simplified model of dynamical perfect plasticity
This paper is devoted to confront two different approaches to the problem of
dynam-ical perfect plasticity. Interpreting this model as a constrained
boundary value Friedrichs' system enables one to derive admissible hyperbolic
boundary conditions. Using variational methods, we show the well-posedness of
this problem in a suitable weak measure theoretic setting. Thanks to the
property of finite speed propagation, we establish a new regularity result for
the solution in short time. Finally, we prove that this variational solution is
actually a solution of the hyperbolic formulation in a suitable
dissipative/entropic sense, and that a partial converse statement holds under
an additional time regularity assumption for the dissipative solutions
Homogenization of variational problems in manifold valued BV-spaces
This paper extends the result of \cite{BM} on the homogenization of integral
functionals with linear growth defined for Sobolev maps taking values in a
given manifold. Through a -convergence analysis, we identify the
homogenized energy in the space of functions of bounded variation. It turns out
to be finite for -maps with values in the manifold. The bulk and Cantor
parts of the energy involve the tangential homogenized density introduced in
\cite{BM}, while the jump part involves an homogenized surface density given by
a geodesic type problem on the manifold.Comment: 32 page
A note on the derivation of rigid-plastic models
This note is devoted to a rigorous derivation of rigid-plasticity as the
limit of elasto-plasticity when the elasticity tends to infinity
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