Une nouvelle analyse des sym\'etries d'un mat\'eriau \'elastique anisotrope. Exemple d'utilisation \`a partir de mesures ultrasonores

TL;DR

This paper presents a method to identify and analyze the symmetry properties of anisotropic elastic materials using ultrasonic measurements and pole figures, enabling the determination of the closest symmetric stiffness tensor.

Contribution

It introduces an intrinsic function to derive the nearest symmetric stiffness tensor and its natural basis from ultrasonic measurements, applicable to anisotropic materials with unknown symmetry.

Findings

Successful application to an oak specimen with 26 faces

Identification of approximate symmetry levels from ultrasonic data

Quantitative measures of tensor distances for symmetry assessment

Abstract

This note deals with stiffness tensors measured from anisotropic linear elastic materials, whose symmetry is unknown. Their possible symmetries (exact or approximative) are revealed by a pole figure. An intrinsic function allows one to obtain a stiffness tensor which posses the chosen symmetry, the nearest from the measured tensor, and its associated natural symmetry basis. For each symmetry level, a distance between these tensors is given. The measurement of the stiffness tensor is done with an ultrasonic direct contact method. It is applied onto a 26 faces oak specimen.