A new macroscopic method of fabric analysis based upon Fresnel’s theorem

Fresnel’s theorem used in optical crystallography is applicable to fabric analysis, strain analysis and stress analysis due to the similarity in formulation between the optical indicatrix, the fabric ellipsoid, the strain ellipsoid and the stress ellipsoid. It describes the relationship between the fabric trace on any section and the circular sections of the fabric ellipsoid. Its explicit expression is equivalent to the expression of the Wallace-Bott hypothesis for stress inversion. A new method is thus developed in this paper to determine the fabric ellipsoid from no less than four independent sectional measurements. Artificial and real examples are taken to illustrate the feasibility of this new method. The advantage of the method over some of the existing graphic methods is that it can deal with any set of sectional measurements.