Determination of Finite Strain and Initial Shape from Deformed Elliptical Objects

Abstract

To determine finite strain from material such as deformed pebbles and oolites, it is essential to consider the initial shape and orientation of the particles. The ellipsoidal objects are studied as ellipses on plane sections. The distribution of axial ratios and orientations of undeformed particles is used as the basis for a classification of initial distributions. Simple and general equations relating the initial and deformed shape and orientation of the particles are derived by considering the matrix algebra. A shape factor grid enables accurate calculation of the magnitude and orientation of the strain ellipse. A variety of important initial distributions can be determined and used. The sudden onset of continuous cleavage and oriented textures observed in some orogenic areas is partially due to the effect of the initial shape of crystals, grains, and clastic particles.