2018/04/18 by Len Bos, Bos, Len, Michael A. Slawiński +3
Engineering · Computer Science · #Composite Material Mechanics #Advanced Mathematical Modeling in Engineering #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1804.06891
As shown by Backus (1962), the average of a stack of isotropic layers results in a transversely isotropic medium. Herein, we consider a stack of layers consisting of a randomly oriented anisotropic elasticity tensor, which-one might expect-would result in an isotropic medium. However, we show-by means of a fundamental symmetry of the Backus average-that the corresponding Backus average is only transversely isotropic and not, in general, isotropic. In the process, we formulate, and use, a relationship between the Backus and Gazis et al. (1963) averages.