MOHR CIRCLES OF THE 1ST-KIND AND 2ND-KIND AND THEIR USE TO REPRESENT TENSOR OPERATIONS

Mohr circles for large irrotational deformations have proved valuable as aids to our understanding deformation geometry. However, confusion persists regarding sign conventions. There are two basic kinds of Mohr circles, each with its distinct set of sign convention. These two divisions, which we call Mohr circles of the First and Second Kind, are not merely reflections of one another in Mohr space. They represent two distinct aspects of the relationship between the space of tensor components (Mohr space) and the space of geological structures (geographical space). The distinction between Mohr circles of the First and Second Kind is critical when the circles are drawn in off-axis positions for asymmetric tensors. Constructions in Mohr space are described which correspond to various standard tensor operations including transportation, inversion, addition and various kinds of multiplication. For some of these operations Mohr circles of one kind or the other offer advantages.