At equation [2b], the linear strain rate associated with sx is composed of two parts, the viscous and diffusive contributions. But the expression of geometrical continuity [4] involves not only linear strain rates but also the shear strain rate g. In a non-diffusing material g = t / N but again, admitting diffusion creates an extra term; the extra term, , is established as follows.

Let a small rectangular element carry stresses sx, sy and t as in Figure A3.4A; then the stress state can be described as a superposition of the two stress states shown in diagram B; here in magnitude the normal stress S equals the original shear stress t. Following the pattern of equation-set [1], we assume that the pair (S, -S) drives linear strain rates and . These generate a shear strain rate in the element in diagram A with magnitude and because S and t are numerically equal, the shear strain rate is also

A fuller discussion of this topic is given in Bayly and Minkel (in press), as Appendix 2 of that work.

Figure A3.4 A general state of stress and an equivalent pair of pure-shear states.