16 research outputs found
Reiterated periodic homogenization of integral functionals with convex and nonstandard growth integrands
Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting.
It is shown by the reiteraded periodic two-scale convergence method that the
sequence of minimizers of a class of highly oscillatory minimizations problems
involving convex functionals, converges to the minimizers of a homogenized
problem with a suitable convex function
A homogenized bending shell theory for multiscale materials from nonlinear elasticity
We derive homogenized bending shell theories starting from three dimensional
nonlinear elasticity. The original three dimensional model contains three small
parameters: the two homogenization scales and of
the material properties and the thickness of the shell. Depending on the
asymptotic ratio of these three parameters, we obtain different asymptotic
theories
Spectral and homogenization problems
Dissertation for the Degree of Doctor of Philosophy in MathematicsFundação para a Ciência e a Tecnologia through the Carnegie Mellon | Portugal Program under Grant SFRH/BD/35695/2007, the Financiamento Base 20010 ISFL–1–297, PTDC/MAT/109973/2009 and UT
Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?
A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works