Engineering Rock Mechanics

Interaction matrices 227

that shear strain involves an interaction between the axes because the
amount of shear strain in the x-axis depends on the position along the y-
axis, cf. Fig. 5.3.
Another example of the way in which interaction matrices can be used
to present information is illustrated in Fig. 14.4. The leading diagonal terms
are a square, a rectangle, a rhombus and a parallelogram. These are four
geometrical shapes which can be converted into one another by either
adding or subtracting the constraints of four equal sides or four equal
angles. The condition boxes shown indicate the constraints necessary to
produce the given shapes from a generic quadrilateral. The off-diagonal
terms are condition icons representing the various transformations
necessary to change one leading diagonal term into another-these
conditions being added or subtracted. When transforming any pair of
leading diagonal shapes from one to another, the same conditions are
involved, whether one is in the upper half of the matrix or the lower half;
only the sign of the condition is different, and hence the matrix is skew-
symmetric. The link with group theory is intimated in the Venn diagram
also presented, but a full discussion of this subject is not necessary here.

4 equal 4 equal

1 <ides I angler I

(01 :subtract a condition

@:add a condition

Figure 14.4 An interaction matrix demonstrating links between

diagonal terms.

the leading