Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended.

"Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended.

Topology Optimization with the Homogenization and the Level-Set Methods.- Thin Films of Active Materials.- The Passage from Discrete to Continuous Variational Problems: a Nonlinear Homogenization Process.- Approaches to Nonconvex Variational Problems of Mechanics.- On G-Compactness of the Beltrami Operators.- Homogenization and Optimal Design in Structural Mechanics.- Homogenization and Design of Functionally Graded Composites for Stiffness and Strength.- Homogenization for Nonlinear Composites in the Light of Numerical Simulations.- Existence and Homogenization for the Problem ?div a(x, Du)=f When a(x, ?) is a Maximal Monotone Graph in ? for Every x.- Optimal Design in 2-D Conductivity for Quadratic Functionals in the Field.- Linear Comparison Methods for Nonlinear Composites.- Models of Microstructure Evolution in Shape Memory Alloys.- Stochastic Homogenization: Convexity and Nonconvexity.