The isotropic material closest to a given anisotropic material
Andrew N. Norris
Abstract
The isotropic elastic moduli closest to a given anisotropic elasticity tensor are defined using three definitions of elastic distance, the standard Frobenius (Euclidean) norm, the Riemannian distance for tensors, and the log-Euclidean norm. The closest moduli are unique for the Riemannian and the log-Euclidean norms, independent of whether the difference in stiffness or compliance is considered. Explicit expressions for the closest bulk and shear moduli are presented for cubic materials, and an algorithm is described for finding them for materials with arbitrary anisotropy. The method is illustrated by application to a variety of materials, which are ranked according to their distance from isotropy.
Create a lesson
Related papers
Temperature dependence of the charge density from first principles: application to the (222) forbidden reflection in silicon
Jean Paul Nery, Raveena Gupta, Olle Hellman et al.
Coupled anisotropic weak topological states and Floquet mixed-parity altermagnetism in two-dimensional Su-Schrieffer-Heeger models
Kunyuan Feng, Xibin Liu, Chenchen Liu et al.
Grain Boundary Phase Transitions Enable Diffusionless Climb of Disconnections
Md Sharier Nazim, Giacomo Po, Nikhil Chandra Admal
3D Cloud Component Analysis of Atomic Structures
Pai Li
Benchmarking of Fast and Interpretable UF Machine Learning Potentials
Pawan Prakash, Sam Dong, Richard G. Hennig
Grain-Boundary Premelting in High-Entropy Transition Metal Carbides
Marium M. Mou, Caleb Schenck, Samuel E. Daigle et al.