Abstract
A new algebraic method is developed to determine the shape and orientation of the strain ellipsoid by using deformed ellipsoidal objects as strain markers. It is assumed that objects are of truly ellipsoidal shape with random orientation in the undeformed state, and that they deform homogeneously with their matrix. This part presents basic theories for: 1. (1) the determination of the strain ellipse on a plane section from deformed elliptical objects; 2. (2) determination of the strain ellipsoid from measurements of lengths and orientations of all principal axes of deformed ellipsoidal objects; and 3. (3) construction of the strain ellipsoid from the two-dimensional analysis on three mutually orthogonal planes. General, finite, homogeneous deformation is treated, and the analysis gives the deviatoric natural strains in the principal directions of the Eulerian finite-strain tensor. The simplicity and usefulness of our method is demonstrated by the two-dimensional, pure-shear deformation of model objects. Evaluation of error and optimum sample size, and geological applications of the method will be discussed in detail in subsequent papers.
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