Initial Geometric Configuration Research Articles

Mechanics of a Hybrid Circular Braid with an Elastic Core

A mathematical model based on four modes of operation is developed to predict the tensile response of a hybrid circular braid encompassing an elastic core. Model inputs include parameters characterizing the initial geometric configuration and ma terial properties of the hybrid. Output parameters are forces, strains, modes of operation, and hybrid geometry. The results show that a hybrid braid can display a unique syn ergism when the braid is in contact with the core but not yet locked, since its tensile response exceeds the sum of its components acting alone. While this analysis idealizes braid geometry and excludes explicit treatment of yam crimp, it incorporates primary influences including nonlinear yam tensile response, large deformations, yam failure, and varying hybrid deformation modes.

A numerical study of the shearing motion of emulsions and foams

A numerical study is presented of the motion of two-dimensional, doubly periodic, dilute and concentrated emulsions of liquid drops with constant surface tension, subject to a simple shear flow. The numerical method is based on a boundary integral formulation that employs a Green's function for doubly periodic Stokes flow, computed using the Ewald summation method. Under the assumption that the viscosity of the drops is equal to that of the ambient fluid, the motion is examined in a broad range of capillary numbers, volume fractions, and initial geometrical configurations. The latter include square and hexagonal lattices of circular and closely packed hexagonal drops with rounded corners. Based on the nature of the asymptotic motion at large times, a phase diagram is constructed separating regions where periodic motion is established, or the emulsion is destabilized due to continued elongation or coalescence of intercepting drops. Comparisons with previous computations for bounded systems illustrate the significance of the walls on the evolution and rheological properties of an emulsion. It is shown that the shearing flow is able to stabilize a concentrated emulsion against the tendency of the drops to become circular and coalesce, thereby allowing for periodic evolution even when the volume fraction of the suspended phase might be close to that for dry foam. This suggests that the imposed shearing flow plays a role similar to that of the disjoining pressure for stationary foam. At high volume fractions, the geometry of the microstructure and flow at the Plateau borders and within the thin films separating adjacent drops are illustrated and discussed with reference to the predictions of the quasi-steady theory of foam. Although the accuracy of certain fundamental assumptions underlying the quasi-steady theory is not confirmed by the numerical results, we find qualitative agreement regarding the basic geometrical features of the evolving microstructure and effective rheological properties of the emulsion.

Rotation Corrections in Three-Point Single Edge Notch Bend Specimens

Abstract In elastic-plastic fracture toughness tests of three-point single edge notch bend (3P-SENB) specimens, very ductile materials suffer significant distortions from their initial geometrical configuration, producing large rotation angles of the arms and causing the rollers to move out and detach themselves. These effects should be taken into account when the Unloading Compliance Method is employed to obtain the slow stable crack growth, because the equations are calculated for the initial condition of null rotation angles. Experimental measurements of the span change for 3P-SENB specimens with different rotation angles and under several conditions were obtained. The results were compared with other authors' results and with those corresponding to CT specimens. Expressions for the corrected values of span and compliance were deduced, and the errors for not using the corrections were estimated. Conditions that give minimal errors were also documented.