DETERMINATION OF THE SYMMETRIES OF AN EXPERIMENTALLY DETERMINED STIFFNESS TENSOR, APPLICATION TO ACOUSTIC MEASUREMENTS

For most materials, the symmetry group is known a priori and deduced f rom the realization process. This allows many simplifications for the measurements of the stiffness tensor. We deal here with the case where the symmetry is a priori unknown, as for biological or geological mat erials, or when the process makes the material symmetry axis uncertain (some composites, monocrystals). The measurements are then more compl icated and the raw stiffness tensor obtained does not exhibit any symm etry in the Voigt's matrical form, as it is expressed in the arbitrari ly chosen specimen's base. A complete ultrasonic measurement of this s tiffness tensor from redundant measurements is proposed. In a second t ime, we show how to make a plane symmetry pole figure able to give vis ual information about the quasi-symmetries of a raw stiffness tensor d etermined by any measurement method. Finally we introduce the concept of distance from a raw stiffness tensor to one of the eight symmetry c lasses available for a stiffness tensor. The method provides the neare st tensor (to the raw stiffness tensor) possessing a chosen symmetry c lass, with its associated natural symmetry base. (C) 1998 Elsevier Sci ence Ltd. All rights reserved.