The incremental flow formulation for the numerical analysis of 3-dimensional viscous deformation processes: continuum formulation and computational aspects

Abstract

The incremental flow formulation recently presented (J. Bonet, The incremental flow formulation for the numerical analysis of plane stress and thin sheet forming processes, Comput. Methods Appl. Mech. Engrg., in press) is applied herein for the analysis of three dimensional viscous deformation processes. Using this technique the equilibrium equations become functions of the nodal positions instead of nodal velocities as in the case of the standard flow formulation. Consequently, geometrical constraints such as the incompressibility of the flow can be enforced in an exact manner. The discretization techniques essential for a successful implementation of this method are also discussed. In particular the element proposed is the 8-noded hexahedron with a mean quadrature integration technique. Finally, some applications relating to the superplastic forming of thick sheet are used to illustrate the effectiveness of the methods presented.