Exact relations for effective tensors of polycrystals by Yury Grabovsky JTB 320 3:20pm, Monday, 20 October, 1997 Abstract The set of all effective moduli of a polycrystal usually has a nonempty interior. When it does not, we say that there is an exact relation for effective moduli. In this talk I will describe a general method for finding such relations. The method is applicable to any physical setting that can be put into the Hilbert space framework developed by Milton (CPAM, 1990). The idea is to find all exact relations that are stable under lamination and then check if they satisfy sufficient conditions, that we have derived, for stability under homogenization. At present it is not know wether necessary conditions are sufficient or not. The power of the method is demonstrated on the examples of 3-D elasticity, piezoelectricity and thermoelectricity. Authors: Yury Grabovsky and Graeme Milton. Order reprints via email to yuri@math.utah.edu and milton@math.utah.edu This information can be found at http://www.math.utah.edu/research/