Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

Extensional orogenic collapse captured by strike-slip tectonics:

The late Paleozoic collision between Gondwana and Laurussia resulted in the polyphase deformation and magmatism that characterizes the Iberian Massif of the Variscan orogen. In the Central Iberian Zone, initial con- tinental thickening (D1; folding and thrusting) was followed by extensional orogenic collapse (D2) responsible for the exhumation of high-grade rocks coeval to the emplacement of granitoids. This study presents a tectonometamorphic analysis of the Trancoso-Pinhel region (Central Iberian Zone) to ex- plain the processes in place during the transition froman extension-dominated state (D2) to a compression-dom- inated one (D3).Wereveal the existence of low-dipping D2 extensional structures later affected by several pulses of subhorizontal shortening, each of them typified by upright folds and strike-slip shearing (D3, D4 and D5, as identified by superimposition of structures). The D2 Pinhel extensional shear zone separates a low-grade domain from an underlying high-grade domain, and it contributed to the thermal reequilibration of the orogen by facil- itating heat advection from lower parts of the crust, crustal thinning, decompression melting, and magma intru- sion. Progressive lessening of the gravitational disequilibrium carried out by this D2 shear zone led to a switch from subhorizontal extension to compression and the eventual cessation and capture of the Pinhel shear zone by strike-slip tectonics during renewed crustal shortening. High-grade domains of the Pinhel shear zone were folded together with low-grade domains to define the current upright folded structure of the Trancoso-Pinhel re- gion, the D3 Tamames-Marofa-Sátão synform. Newdating of syn-orogenic granitoids (SHRIMP U\\Pb zircon dat- ing) intruding the Pinhel shear zone, together with the already published ages of early extensional fabrics constrain the functioning of this shear zone to ca. 331–311 Ma, with maximum tectonomagmatic activity at ca. 321–317 Ma. The capture and apparent cessation of movement of the Pinhel shear zone occurred at ca. 317– 311 Ma.