Screw periodic boundary condition

Fig. 65. (a) Boundary conditions used to impose at tilled interface in an Ising ferromagnet antiperiodic (APBC) in the z-direction, periodic in the y-direction (PBC), and screw periodic boundary conditions (SPBC) in the x-direction. 

Because the geometry of a double-flighted screw element repeats after half the pitch, it is sufficient to observe a length of 60 mm. Assuming a fully developed, isothermal flow, the upper and lower cross-section surfaces are linked together by periodic boundary conditions. 

In its current implementation, the CADD method can only deal with 2D problems, i.e., problems where the dislocations all have a line direction perpendicular to the modeled plane. However, the method does not contain any limitation on the dislocation character (edge, screw, or mixed) because periodic boundary conditions along the z direction are used in the atomistic region and three degrees of freedom (displacements U , Uy, and u ) are considered in the two-dimensional (x-y) continuum region. The extension of the methodology to the 3D case is not trivial and is currently being explored. 

Since a standard screw geometry within a cooling extruder has a periodic flow chaimel, a periodic inflow/outflow boundary condition is applied to simulate fully developed flow. Validation tests showed that a single pitch of the screw with poiodic boundary conditions is sufficient to model polymer melt flow behavior in the whole cooling screw geometry. 

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