MATLAB code for Log-Euclidean Estimates of Piezoelectric Polycrystals

Description

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.

Steps to reproduce

The numerical results and code implementation are based on the theoretical framework and closed-form orientation-averaging expressions detailed in the associated research article: "A Fast Log-Euclidean One-Point Estimate for Coupled Electromechanical Polycrystals: Spectral Bounds, Inversion Consistency, and Limits of Loewner Ordering" (2026).

Institutions

• Universidad de Sevilla

  Andalusia, Seville

Categories

Funders

• Ministerio de Ciencia, Innovación y Universidades

  Madrid, Madrid

  Grant ID: Project PID2022-137903OBI00, funded by MICIU/AEI/10.13039/501100011033/ and by ERDF/EU.

Licence