DETERMINATION OF THE STRAIN ELLIPSOID FROM SECTIONAL DATA

This paper presents a new way to determine the shape and orientation of the triaxial strain ellipsoid, given sectional strain data from at least three arbitrary planes. First the sectional strain ellipses are scaled to maximize compatibility along their lines of intersection. Then, using formulae for strain determination from three known stretches, the sectional strain ellipse is calculated for a 'fourth' plane chosen to intersect the data planes at the highest possible angles. By repeated sectional strain determination in a set of test planes oriented perpendicular to the above fourth plane, the triaxial strain state is revealed. The longest test sectional strain ellipse long axis is the strain ellipsoid's long axis and the shortest test sectional strain ellipse short axis is the strain ellipsoid's short axis. The strain ellipsoid's intermediate axis is the pole to the plane of maximal and minimal stretches and its stretch is calculated in the test plane in which it lies. Manual calculations, while easily understood, are time-consuming, requiring several hours for one triaxial strain determination, but a set of computer programs is available from the author. Accuracy is evaluated by determining the strain state in the data planes given the calculated triaxial ellipsoid's principal sections, and comparing results of such determinations with the observed data. © 1990.