Composite media and homogenization theory : an International Centre for Theoretical Physics workshop, Trieste, Italy, January 1990

This volume contains the Proceedings of the Workshop on Composite Media and Homogenization Theory held in Trieste, Italy, from January 15 to 26, 1990. The workshop was organized by the International Centre for Theo- retical Physics (ICTP); part of the activity was co-sponsored by the Interna- tional School for Advanced Studies (SISSA). The workshop covered a broad range of topics in the mathematical the- ory of composite materials and homogenization. Among the specific areas of focus were homogenization of periodic and nonperiodic structures, porous me- dia, asymptotic analysis for linear and nonlinear problems, optimal bounds for effective moduli, waves in composite materials, optimal design and relaxation, random media. The workshop was actively attended by more than 100 participants from 23 countries. In the afternoon sessions 35 seminars were delivered by the participants. This volume contains research articles corresponding to 14 of the 20 invited talks which were presented. Its content will be of interest both to mathematicians working in the field and to applied mathematicians and engineers interested in modelling the behaviour of composite and random media We are pleased to express here our thanks to the ICTP for having made this workshop possible, to Ms. A. Bergamo for her continuous help during the workshop, and to Ms. C. Parma for her collaboration in editing the proceedings. Gianni Dal Maso Gian Fausto Dell'Antonio SIS SA, Trieste Universita "La Sapienza," Roma v Contents Preface ................................................................................ v List of Speakers ..................................................................... ix Contributors .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii . . . . . . . . . . . . . . . . . . . . . . . . . . Front Matter....Pages i-xiv Integral Representation of Functionals Defined on Sobolev Spaces....Pages 1-12 Homogenization and Renormalization of Multiple-Scattering Expansions for Green Functions in Turbulent Transport....Pages 13-35 Properties of Averaged Models of the Periodic Media Mechanics....Pages 37-46 Homogenization of a Class of Stochastic Partial Differential Equations....Pages 47-65 Effective Medium Approximation for Nonlinear Conductivity of a Composite Medium....Pages 67-79 Homogenization of Nonlinear Unilateral Problems....Pages 81-105 Homogenization, Plasticity and Yield Design....Pages 107-133 Some remarks on Γ-convergence and least squares method....Pages 135-142 Homogenization of Miscible Displacement in Unsaturated Aggregated Soils....Pages 143-158 Homogenized Models of Composite Media....Pages 159-182 Structural Optimization of a Linearly Elastic Structure using the Homogenization Method....Pages 183-203 Geometry and asymptotics in homogenization....Pages 205-221 The Field Equation Recursion Method....Pages 223-245 Composite media and Dirichlet forms....Pages 247-258 Back Matter....Pages 259-259