Monday, May 12

10:30 AM-12:10 PM
Peale C Room

MS2
Effective Properties of Nonlinear Composites

Nonlinear homogenization is of great interest in many applications, including polycrystalline plasticity and nonlinear optics. Although many successful methods have been developed to estimate the effective behavior of linear composites, it is only recently that general nonlinear homogenization methods have been advanced. These include variational methods based on the use of a linear comparison composite, asymptotic methods and numerical methods. Although the variational methods are quite powerful, they suffer from certain limitations. For example, whereas certain linear estimates are known to be exact to second-order, the corresponding nonlinear estimates are only exact to first order. On the other hand, it is possible to obtain perturbation estimates that are exact to second order. Unfortunately, the range of validity of these asymptotic estimates can vanish for strong enough nonlinearity. Computational estimates can fill the gap, and point the way for future improvement in the analytical estimates. The speakers will present recent developments in these general areas.

Organizer: Pedro Ponte Castaneda
University of Pennsylvania

10:30-10:50 Numerical Simulation of the Linear and Nonlinear Overall Properties of Cell-Materials

Pierre Suquet and H. Moulinec, Laboratoire de Mecanique et d'Acoustique, France

10:55-11:15 Nonlinear Homogenization and Polycrystal Plasticity

Robert V. Kohn and Thomas Little, Courant Institute of Mathematical Sciences, New York University

11:20-11:40 Enhanced Nonlinearity and Dielectric Hysteresis in Composite Materials

Ohad Levy, Courant Institute of Mathematical Sciences, New York University

11:45-12:05 Variational Methods for Estimating Nonlinear Effective Behavior

Pedro Ponte Castaneda, Organizer

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