Construction and computation of three-dimensional progressive deformations

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Abstract
The deformation plot is shown to be ideal for the display of ellipsoid shape, as is its logarithmic transformation for the display of deformation paths of coaxial deformations. Other plots which have been proposed can be derived from the deformation plot by various geometric transformations and by the superposition of other coordinate axes. These variants of the deformation plot are less convenient to use. The deformation plot may also be used for the construction of deformation paths. This use depends on the definition of a number of different types of deformation ellipsoid. In particular, in deformations involving volume change, the shape change arising from the volume change needs to be represented by an ellipsoid. Under these conditions coaxial deformation paths of any imaginable complexity can be easily constructed on the deformation plot. For non-coaxial deformation, matrix representation of the deformation ellipsoids allows deformation paths to be computed, but graphic representation of these results requires both the deformation plot and a stereonet.