Driving stress

The deformation is assumed to result in chain slippage but some chain entanglement will influence the mechanical response. This feature is assumed to be lumped into the parameters q and m so that no back stress contribution appears above Tg. Therefore, the driving stress reduces to a = o and the equivalent shear stress x in (4) is that of the Cauchy stress o. 

Shear yielding in the bulk of the material is incorporated through the constitutive law presented in the previous section. The definition of the plastic strain rate CP together with the expression for the driving stress 6 specifies the energy dissipation rate per unit volume G D< = /2tY . The energy balance in the material can then be written as... 

On the other hand, suppose the 1 mm shortening were a purely viscous effect that required 10 seconds of applied stress what would be the viscosity of the material The driving stress difference is still 0.06 MPa, but the denominator needed (eqn. 7.8b) is now a strain rate 3/3200 per sec. Hence 2N = 64 MPa-sec or 3840 MPa-min or 64 x 10 Pa-sec or 64 x 10 poise. 

The analyses emphasize the idea that when a volume-element changes volume by diffusive mass transfer at constant density, the change is not isotropic the strain components Cyy, and e are linked by three separate equations to the components and gradients of the driving stress field. 

If two phases with viscosities and Nf, are constricted at the same radial strain rate Cq, the driving stress differences in the two phases are 6eoAg and 6e()Nf. If the stress states have a common stress the two magnitudes of will differ by 6eo(Ng — Nf,). If is, for example, Ag/lO, the order of... 

Pile driving formulas are generally considered as unreliable. The alternative is to use the dynamics of pile driving in more detail, and this method is called the wave equation method. This method provides a more accurate function of capacity versus blow count helps optimize the driving equipment, and computes driving stresses. 

Equation (5.3) represents the magnitude of the amorphous inelastic strain rate, while the direction of the amorphous inelastic flow rate,, is governed by the deviatoric driving stress, s y. The following flow rule is proposed for the inelastic deformation in the amorphous phase [88] ... 

In the above equation, K represents the crack driving stress intensity in any general direction, is the driving force in the x direction, and a is the angle of inclination of the crack direction to the x direction. 

Tranos MD, Lacombe O (2014) Late Cenozoic faulting in SW Bulgaria fault geometry, kinematics and driving stress regimes. Implications for late orogenic processes in the Hellenic hinterland. J Geodyn... 

Figure 4 shows driving stress, calculated from ice thickness and surface slope, and surface velocity along a flow-line in the southern part of the Greenland Ice Sheet. The curves have the expected shape. The driving stress increases from zero at the ice divide to about 100 kPa at a distance of 50 km, a value that is maintained until the ice thins near the terminus. The maximum velocity is at the equilibrium line. 

Fig. 4. Computed driving stress and surface velocity along a typical flow-line in south Greenland. The equilibrium line is at 165 km from the ice divide, fkom Dahl-Jensen (1989).

Fig. 6. Driving stress and surface velocity along a flow-line in the West Antarctic Ice Sheet. The flow-line starts in the inland ice, runs along Ice Stream B, and then through a transition zone into the floating Ross Ice Shdf. From Alley and Whillans (1991) by permission of the American Association for the Advancement of Science.

Here is the driving stress, R the bed roughness (amplitude of bumps divided by their spacing), n (=3) the index in the fiow relation and B a constant that depends on the thermal and mechanical properties of the ice. This equation cannot be used for prediction because bed roughnesses are seldom, if ever, known. 

The total stress is additively decomposed into a driving stress (indicated by s) and a hardening stress (indicated by r) (eqn [tl]) ... 

The driving stress is further subdivided into a hydrostatic (h) and a deviatoric (d) contribution ... 

The deviatoric contribution of the driving stress acts on both the elastic spring and the plastic dashpot since they are placed in series and can therefore be given by... 

In the case of incompressibility, the volume change factor / is unity, and therefore the hydrostatic contribution of the driving stress is zero of = 0. The total stress can now be given by... 

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