MATLAB code for Log-Euclidean Estimates of Piezoelectric Polycrystals

This repository contains the supplementary material for the research article: "A Fast Log-Euclidean One-Point Estimate for Coupled Electromechanical Polycrystals: Spectral Bounds, Inversion Consistency, and Limits of Loewner Ordering" (2026). It provides a MATLAB implementation of the log–Euclidean geometric-mean one-point estimate for coupled electromechanical polycrystals. The code computes texture coefficients, evaluates the Voigt average of the matrix logarithm of the 9×9 Kelvin–Mandel extended constitutive operator using closed-form orientation averages for tetragonal 4mm crystals, and returns the effective tensor via the matrix exponential. Additionally, the code computes the classical Voigt and Reuss estimates to define the bounds discussed in the study. The repository includes a reproducible workflow matching the algorithm reported in the associated manuscript. For detailed file descriptions and execution instructions, please refer to the README.md file included in the repository.