Marco Barchiesi, Department of Mathematical Sciences, Carnegie Mellon University.
Homogenization of polyconvex functionals
Using two-scale Young measures, I will describe the zero level set of an effective energy density related to a periodic microstructure. I will use this analysis to show that polyconvex energies are not closed with respect to periodic homogenization. The counter-example is based on a rank-one laminated structure obtained by mixing two polyconvex functions with $p$-growth, where $p\geq2$ can be fixed arbitrarily. I will also discuss a counter-example to the continuity of the determinant with respect to two-scale convergence.
TUESDAY, October 16, 2007