Homogenisation in finite elasticity for composites with a high contrast in the vicinity of rigid-body motions
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Mon, 28/11/2011 17:00 |
Kirill Cherednichenko (Cardiff University) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
I will describe a multiscale asymptotic framework for the analysis of the macroscopic behaviour of periodic
two-material composites with high contrast in a finite-strain setting. I will start by introducing the nonlinear
description of a composite consisting of a stiff material matrix and soft, periodically distributed inclusions. I shall then focus
on the loading regimes when the applied load is small or of order one in terms of the period of the composite structure.
I will show that this corresponds to the situation when the displacements on the stiff component are situated in the vicinity
of a rigid-body motion. This allows to replace, in the homogenisation limit, the nonlinear material law of the stiff component
by its linearised version. As a main result, I derive (rigorously in the spirit of  -convergence) a limit functional
that allows to establish a precise two-scale expansion for minimising sequences. This is joint work with M. Cherdantsev and
S. Neukamm. |
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