THE SIMPLE FLUID WITH FADING MEMORY AS A RHEOLOGICAL MODEL FOR STEADY-STATE FLOW OF ROCKS

Abstract

The phenomenological approach to determining constitutive equations has rarely shown itself capable of producing predictive descriptions of complex materials. The equations used in geology are essentially of the form ▪ where the stress T at a given (x, t) is entirely determined by the rate-of-deformation D at that instant in time. H may be linear or non-linear but deformations taking place at other times are assumed to be irrelevant. Rocks are manifestly more complicated than this and a more general axiomatic model - the simple fluid - is outlined in this paper in which the stress at (x, t) is determined by the entire history of D. In particular we examine some restrictions imposed by deformation geometry, and by the ‘fading memory’ approximation for very slow flows. Some implications for rigid crystal rotations in porphyroblastic rocks are considered: the classical analysis here assumes a Newtonian rock matrix and we explore the effects of employing, instead, a simple fluid with fading memory model.