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Sets of conductivity and elasticity tensors stable under lamination
Gilles A. Francfort (Carnegie Mellon University), Graeme Walter Milton (Courant Institute of Mathematical Sciences)
Abstract: Abstract A complete characterization is obtained of any set of constitutive (conductivity or elasticity) tensors that is stable under lamination between any two of the elements of the set. The conditions are local and are expressed in terms of the curvature and tangent plane at points on the boundary of the set. They are checked to hold for several well‐known examples of sets stable under a more general process of homogenization. A companion paper investigates the link between these conditions and quasiconvexity. © 1994 John Wiley & Sons, Inc.