This means that for a rock element subjected to tri-axial stresses, 0x, 0y, 0z, it will be assumed that failure is a function of the second stress invariant function
With the first invariant function f estimated, we are able to plot the second invariant function g from the compression stress values [[sigma].
This first approximation confirms the form of the second invariant function g([I.
0] factor uncontracted in any tensorial fashion, and demonstrate causality of the gauge invariant functions of the field.
The latter has been verified for packets using gauge invariant functions of the fields.
We will extend the lagrangian with auxiliary fields so that this is not necessary but only that the gauge invariant functions of the collective reality of these fields evolve causally.
Canonical decomposition of nonlinear dynamic systems based on invariant functions
Appendixes cover topics that are not standard parts of an average science of engineering undergraduate curriculum: Green's functions, real spherical harmonics, spherical modified Bessel functions, plane groups and invariant functions
, and elementary elasticity theory.