In uniaxial tensile tests of low-carbon steel sheets conducted by Stickels and Mould, the directional dependence of the r-value (a material parameter used in metal forming) and of the Young's modulus (an elastic constant) were found to be correlated. This phenomenon is sometimes called "correlation of elastic and plastic anisotropy" in the literature. In this talk I will present a simple theory that explains the physical basis behind this phenomenon, which will serve also as an introduction to quantitative texture analysis in metal forming.

In this talk, a generic class of metamaterials is introduced and is shown to exhibit frequency dependent double negative effective properties.  Explicit power series are developed for the dispersion relation and associated Bloch wave solutions on some frequency intervals. These intervals are explicitly determined by two distinct spectra: the Dirichlet spectrum of the Laplacian and the generalized electrostatic spectrum. Direct numerical simulations  show that the leading order term in the power series for the dispersion relation is a good predictor of the dispersive behavior of the metamaterial.