¯ is trace-less One can easily show that the tensor Q 1 Tr(3ˆ ui ⊗ u ˆi − ½) 2 1 = 3 · 1 − 3 = 0 2 ¯= TrQ (91) (92) ¯ is clearly symmetric and hence diagonalizable with three Furthermore Q eigenvalues λ1 ≥ λ2 ≥ λ3 where λ3 must be −λ2 −λ1 . The largest eigenvalue λ1 is called nematic order parameter S.

WEISSENBERG NUMBER - Thermopedia A non-Newtonian Fluid is one for which stress is not linearly related to strain-rate. All non-Newtonian fluids are elasticoviscous, that is they combine elastic and viscous properties.When the time-scale of a flow t f is much less than the relaxation time t r of an elasticoviscous material, elastic effects dominate. When on the other hand t f is much greater than t r, elastic effects relax A reappraisal of the Sibson-Scholz fault zone model: The quartzo-feldspathic crust the frictional-viscous transition is expected to occur in the midcrust, at-10-15 km depth, al- though its exact depth range will depend on a number of fac- tors, including ambient geothermal gradient, strain rate, mode of faulting, pore-fluid pressure [Sibson, 1983; Scholz, 1988],

Lecture 1: Introduction

A non-Newtonian Fluid is one for which stress is not linearly related to strain-rate. All non-Newtonian fluids are elasticoviscous, that is they combine elastic and viscous properties.When the time-scale of a flow t f is much less than the relaxation time t r of an elasticoviscous material, elastic effects dominate. When on the other hand t f is much greater than t r, elastic effects relax A reappraisal of the Sibson-Scholz fault zone model: The

Mechanics of Biological Tissue G.A. Holzapfel R.W. Ogden (Eds.) Mechanics of Biological Tissue With 212 Figures and 14 Tables 123 Professor Gerhard A. Holzapfel Graz University of Technology Institute for Structural Analysis, Computational Biomechanics Schiesstattgasse 14-B, 8010 Graz, Austria E-mail: [email protected]

where the trace less viscous strain rate is given by: ( 5 ) Reichard et al. [22] presented droplet sizes ranging from 1 48 to 424 μ m diameter and wind For a Newtonian uid, assuming Stokes Law for mono-atomic gases, the viscous stress is given by (4): ij = 2 Sij (4) Where the trace-less viscous strain-rate is de ned by (5): ! @ui + @uj ; 1 @uk Sij = 21 @x 3 @xk ij j @xi def (5) The heat- ux, qj , is given by Fourier's law (6): @T ;C @T qj = ; @x p Pr @x j j 11 (6) S Trace-less viscous strain-rate. T Temperature. ~u Velocity vector. X Computational mesh. Subscripts 1 Free-stream condition. ~n Normal component. ref Reference