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02/19/04 Colloquium
DR. MARIAN BOCEA
DEPARTMENT OF MATHEMATICS
CARNEGIE MELLON UNIVERSITY
DEPARTMENT OF MATHEMATICS
CARNEGIE MELLON UNIVERSITY
A Young Measure Approach to Nonlinear Membrane Theory
Abstract: Because of their potential applications as microactuators, martensitic thin films have received much attention in recent years. In view of these applications it is essential to rigorously understand how the thin film theory relates to its three-dimensional counterpart. In this context, the integral representation of relaxed functionals arising in the derivation of nonlinear membrane models for heterogeneous hyperelastic materials is obtained in terms of Young measures. The key technical ingredient is a decomposition result for sequences of scaled gradients, where oscillation and concentration effects are separated.